Cs corrector

The Cs corrector is a device for correcting spherical aberrations , C _s , in the optics of charged particles ( electron optics, ion optics). The development of such systems was mainly driven by possible applications in the field of electron microscopy .

Spherical aberration in the electron microscope

In particle-optical systems, rotationally symmetrical lenses are used, which usually have a magnetostatic, less often an electrostatic structure. The theory of electron optics shows that rotationally symmetrical electromagnetic lenses with fields that are constant over time cannot be manufactured without spherical aberrations due to their principle. The coefficient of spherical aberration of a magnetic rotationally symmetric lens depends on the maximum field strength in the lens. This is limited by the saturation behavior of the material used for the lens.

Cs EM 01 png

The lowest order of the spherical aberrations is the third, here reference is made to the dependence of the transverse deviation on the aperture angle (see also spherical aberration , but there the change in back focus due to the aberration is considered). For small it results: ${\displaystyle r_{s}}$ ${\displaystyle \alpha }$ ${\displaystyle \alpha }$

${\displaystyle r_{\rm {s}}=c_{\rm {s}}\alpha ^{3}}$

The third-order spherical aberration is decisive for small ones and at the same time the easiest to correct. The resolution of the electron microscope is determined by the objective lens. This value increases with the opening angle, so the resolution becomes worse. On the other hand, due to the diffraction criterion, you have to work with larger opening angles for higher resolutions. This results in an optimum opening angle of the order of magnitude below 0.01 (0.01  rad ); the exact value depends on the size of the spherical aberration coefficient. Due to diffraction, the resolution limit is at most about 60 times the electron wavelength (example: wavelength 0.0037 nm at 100 keV electron energy, achievable resolution about 0.2 nm). The resolution limit also depends on the coherence of the electrons. Therefore, reducing spherical aberration is critical to improving the resolution of transmission electron microscopes. ${\displaystyle \alpha }$ ${\displaystyle r_{\rm {s}}(\alpha )}$

functionality

While in light optics the correction of spherical aberrations can be achieved by choosing a suitable rotationally symmetrical lens system with aspherical lens geometry, in particle optics the field of rotationally symmetrical lenses cannot be designed in such a way that the aberrations disappear. By using magnetic multipole elements in the beam path, the imaging errors can be compensated so that the usable opening angle of the optics is larger. This is only possible with a computer-based analysis of the original errors and the most precise control of the multipoles. Due to their design, the multipole elements must not be part of the lens to be corrected.

Hexapole and quadrupole-octupole correctors are currently in use. As the number of poles increases, terms of a higher degree appear in the field profiles in the xy -plane (i.e. perpendicular to the optical axis, z ), which leads to higher-order aberration coefficients that change their sign in the xy -plane according to their symmetry: Octupole with n = 8 have a negative aberration coefficient in four octants and a positive one in the four intervening octants. We assume that the octants of the positive cross section lie exactly in the x or y direction. Using quadrupoles, the electron beam can then be shaped once into a line focus in the x direction and once into a line focus in the y direction and thus sent through an octupole each. The beam is then made round again by another quadrupole and then has an overall negative spherical aberration that compensates for the positive aberration of the objective. Since the octupoles also cause 4-fold astigmatism, a third octupole is used to correct it, through which the beam is guided round and with a relatively small diameter.

application

Magnets of a STEM third order Cs corrector

The limit of the resolving power of transmission electron microscopes without a Cs corrector is roughly in the range of the atomic distances in solids (typically around 0.2 nm). Due to the interaction of the electrons with the solid body, a transmission electron microscope (TEM) or a scanning transmission electron microscope (STEM) generally cannot depict individual atoms of a solid, but in a simple way only the projection of the atomic nuclei (or their electrical potentials) in the direction of the electron beam .

If one considers z. If, for example, from a great distance a regular arrangement of balls in a wire mesh, one looks from certain directions on balls lying exactly one behind the other (so-called columns). From slightly different directions, these columns overlap in the picture and cover each other. But the directions from which columns can be seen (the so-called zone axes of the crystal) differ in the distance from which the columns can be seen. These distances between the projected columns are usually smaller than the distances between the spheres, and at most the same size. Hence the need to increase the resolution of the TEM and STEM as far as possible below the actual atomic spacing in order to be able to image crystal lattices from as many directions as possible and the atomic columns separately.

The Cs correctors correct lower order errors (the maximum order is given by the number of multipoles ), but introduce additional higher order errors. In practice, the usable opening of the microscope objective, and thus the spatial resolution, is roughly doubled or tripled, provided that the stability of the device allows this.

Cs correctors were first developed by Zach and Haider for special low-energy scanning electron microscopes (SEMs or LVSEMs), then by Rose and Haider for TEM and by Krivanek for STEM.

literature

• Andrew Bleloch, Andrew Lupini: Imaging at the picoscale . In: Materials Today . tape 7 , no. December 12 , 2004, pp. 42-48 , doi : 10.1016 / S1369-7021 (04) 00570-X .

Web links

• SuperSTEM Laboratory, Daresbury, UK: Introduction to Spherical Aberration Correction in Electron Microscopes.

Individual evidence

1. ↑ O. Scherzer: About some defects in electron lenses . In: Journal of Physics . tape 101 , no. 9-10 , September 1, 1936, pp. 593-603 , doi : 10.1007 / BF01349606 .
2. ^ RF Egerton: Physical Principles of Electron Microscopy. Springer, 2005, ISBN 0-387-25800-0 , p. 49.
3. ^ J. Zach, M. Haider: Correction of spherical and chromatic aberrations in a LVSEM. In: B. Jouffrey, C. Colliex, JP Chevalier, F. Glas, PW Hawkes, D. Hernandez-Verdun, J. Schrevel, D. Thomas (Eds.): Proc. 13th Int. Congr. Electron Microscopy, Paris, France. vol. 1, Editions de Physique, les Ulis, Paris 1994, pp. 199-200.
4. ↑ Harald Rose: Outline of a spherically corrected semiaplanatic medium-voltage transmission electron-microscope . In: Optics . tape 85 , no. 1 , 1990, p. 19-24 .
5. ↑ Maximilian Haider, Herald Rose, Stephan Uhlemann, Bernd Kabius, Knut Urban: Towards 0.1 nm resolution with the first spherically corrected transmission electron microscope . In: Journal of Electron Microscopy . tape 47 , no. 5 , January 1, 1998, pp. 395-405 .
6. ↑ OL Krivanek, N. Dellby, AJ Spence, RA Camps, LM Brown: Aberration correction in the STEM . In: JM Rodenburg (Ed.): Electron Microscopy and Analysis 1997, Proceedings of the Institute of Physics Electron Microscopy and Analysis Group Conference, University of Cambridge, September 2-5, 1997 . CRC Press, 1997, ISBN 0-7503-0441-3 , pp. 35–40 ( limited preview in Google Book search).
7. ↑ OL Krivanek, N. Dellby, AR Lupini: Towards sub-Å electron beams . In: Ultramicroscopy . tape 78 , no. 1-4 , June 1999, pp. 1-11 , doi : 10.1016 / S0304-3991 (99) 00013-3 .