Dynamic Aberration Correction

A. Oelsner (now Surface Concept GmbH), H. Spiecker (now LaVision Biotec GmbH), G. Schönhense

The main factors limiting resolution in electron microscopy are the chromatic and spherical aberrations of round lenses. Astigmatism may result from misalignment or from limitations in manufacturing tolerance (e.g. a slight ellipticity of the anode bore in a tetrode objective lens) and can be compensated by electric or magnetic stigmators. Coma and field distortion are often of minor importance. However, in contrast to light optics the chromatic and spherical aberrations cannot be corrected by lens combinations. Independent of type and geometry of a round lens, the spherical aberration coefficient cs and the chromatic aberration coefficient cc are always positive. This fundamental property of all electron-optical round lenses is referred to as Scherzer’s theorem. As a consequence, the ray paths in electron microscopes are usually restricted by very small aperture diaphragms.

Scherzer himself searched for possible ways out of this dilemma and discussed various possibilities for the correction of cs and cc. The preconditions for the validity of Scherzer’s theorem are: round lenses, real images, static fields, no space charge, and the potential and its derivative are continuous. This list opens ways to circumvent the theorem. Multipole correctors in high-resolution transmission electron microscopy and scanning electron microscopy as well as mirror correctors in low-energy microscopy have set new standards.

Our time-of-flight approach is especially useful for PEEM and LEEM. As the time of flight scales with E1/2, it offers various possibilities to increase the lateral resolution. Gated detection, i.e. time-of-flight filtering, is equivalent to energy filtering and can improve the resolution considerably, see Fig.1. Going one step further, a novel approach for correction of the chromatic and spherical aberration of round-lens systems in PEEM and LEEM is also based on the time of flight. The method employs time-resolved image detection and/or fast switching of electrical acceleration fields or lens fields. It can exploit the highly precise time structure of pulsed photon sources like synchrotron radiation or short-pulse lasers as well as pulsed photocathodes of a LEEM. These sources are characterized by ultimate precision in terms of negligible deviations from periodicity (jitter). Pulse widths can be as low as a few picoseconds for synchrotron radiation and several ten femtoseconds for laser sources.

When using a pulsed excitation source in a PEEM, the photon time structure translates into corresponding parameters of the electron beam. This opens up new technical possibilities far beyond the microwave-modulated electron beams of the early days of high-frequency lenses. First results indicate that the new approach is a promising alternative to the implementation of multipole or mirror correctors into the electron-optical column of a microscope, a first example is shown in Fig.2.

The principles of dynamic chromatic and spherical aberration correction is discussed in [1,2]. For a review, see [3]. A crucial element of the chromatic corrector is the time-resolving image detector, in our case a delayline detector [4]. The spherical corrector resembles an optical achromat, where the diverging lens action is obtained by rapid switching of a lens element. Very short switching times are mandatory for this type of corrector. For rapidly switched electrostatic lenses an additional lens action arises as a consequence of the induced magnetic ring field. We have quantitatively derived this influence on the basis of Maxwell’s equation curlB µ dE/dt. For typical switching times with voltage gradients of about 1000 V /ns and typical lens geometries this lens action can be neglected in comparison with the electrostatic lens action. It is worth noting that the conditions for ion optics are much less critical because the mass is three orders of magnitude higher than for electrons. Thus the temporal dispersion is much higher for ions.

[1] G. Schönhense and H. Spiecker; Correction of Chromatic and Spherical Aberrations in Electron Microscopy Utilizing the Time-Structure of Pulsed Excitation Sources; J. Vac. Sci. Technol. B 20 (2002) 2526-2534
[2] G. Schönhense and H. Spiecker; Array for Achromatic Imaging of a Pulsed Particle Beam, US Patent 6,737,647 B2; and Anordnung zur Abbildung des von einer Probe gepulst emittierten Teilchenensembles auf einem Detektor, German Patent  DE 102 17 507 B4
[3] G. Schönhense, H. J. Elmers, S. A. Nepijko, C. M. Schneider; Time-Resolved Photoemission Electron Microscopy; In: Advances in Imaging and Electron Physics(Ed. P. Hawkes) 142 (2006) 159-323
[4] A. Oelsner, O. Schmidt, M. Schicketanz, M.J. Klais, G. Schönhense, V. Mergel, O. Jagutzki, H. Schmidt-Böcking; Microspectroscopy and  Imaging Using a Delayline-Detector in Time-of-Flight Photoemission Microscopy; Rev. Sci. Instrum. 72 (2001) 3968-3974


Figure 1: ToF energy filtering of a PEEM image (the simplest imaging energy filter).


Figure 2: ToF aberration correction of a PEEM image (from the homepage of Surface Concept GmbH).


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