Stigmator

A stigmator is a component of electron microscopes that reduces astigmatism of the beam by imposing a weak electric or magnetic quadrupole field on the electron beam.

For the photographic lens astigmatism correction lens see Anastigmat.

Background

Quadrupole field created by four wires. The principle of a stigmator is that the current through each of the wires would be adjusted to change the shape of the beam.

For early electron microscopes - between the 1940s and 1960s[1] - astigmatism was one of the main performance limiting factors.[2] Sources of this astigmatism include misaligned objectives, non-uniform magnetic fields of the lenses, lenses that aren't perfectly circular and contamination on the objective aperture.[3][4][5] Especially the astigmatism induced by the non-uniform magnetic fields - which in turn causes non-uniform lens strength - was hard to prevent. Therefore, to improve the resolving resolution, the astigmatism had to be corrected.[6] The first commercially used stigmators on electron microscopes were installed in the early 1960s.[1]

The stigmatic correction is done using an electric or magnetic field perpendicular to the beam.[7] By adjusting the magnitude and azimuth of the stigmator field, asymmetric astigmatization can be compensated for.[5] Stigmators produce weak fields compared to the electromagnetic lenses they correct, as usually only minor correction are necessary.[8]

Number of poles

Stigmators create a quadrupole field, and thus have to consist of at least four poles, but hexapole,[9] octopole and 12-pole stigmatizors are also used, with octopole stigmators being the most common.[10][11] The octopole (or higher order of poles) stigmatizers also produce a quadrupole field, but use their additional poles to align the imposed field with the direction of the stigmatization ellipticity.[3]

Types

Magnetic stigmator

The magnetic stigmator is a weak cylindrical lens that can correct the cylindrical component of the beam. It can consist of metal rods which induce an magnetic field, which are inserted with their long axis towards the beam center. By retracting or extending the rods, the astigmatism can be compensated.[12]

Electromagnetic

Electromagnetic stigmators are stigmators that are integrated with the lenses and directly deform the magnetic field of the lens(es). These were the first types of stigmators to be used.[9][12]

Automatic stigmators

In most cases, the astigmatism can be corrected using a constant stigmator field which is adjusted by the microscope operator. The main cause of astigmatism, the non-uniform magnetic field produced by the lenses, usually does not change noticeable during a TEM session. A recent development are computer-controlled stigmators, which usually use the Fourier transform of the image to find the ideal stigmator setting. The Fourier transform of an astigmatic image is usually elliptically shaped.[13] For a stigmatic image, it is round, this property can be used by algorithms to reduce the astigmatic aberration.[4]

Multiple stigmator systems

Normally, one stigmator is sufficient, but TEMs normally contain three stigmators: one to stigmatize the source beam, one to stigmatize real-space images, and one to stigmatize diffraction patterns. These are commonly referred to as condensor, objective, and intermediate (or diffraction) stigmators.[14] The use of three post-sample stigmators is proposed to reduce linear distortion[15]

References

1. Jon Orloff (24 October 2008). Handbook of Charged Particle Optics, Second Edition. CRC Press. p. 130. ISBN 978-1-4200-4555-0.
2. Peter W. Hawkes (6 November 2013). The Beginnings of Electron Microscopy. Elsevier Science. ISBN 978-1-4832-8465-1.
3. Jon Orloff (24 October 2008). Handbook of Charged Particle Optics, Second Edition. CRC Press. p. 292. ISBN 978-1-4200-4555-0.
4. Batten, C. F. (2000). Autofocusing and astigmatism correction in the scanning electron microscope (Doctoral dissertation, Faculty of the Department of Engineering, University of Cambridge).
5. Elizabeth M. Slayter; Henry S. Slayter (30 October 1992). Light and Electron Microscopy. Cambridge University Press. p. 240. ISBN 978-0-521-33948-3.
6. Hillier, James; Ramberg, E. G. (1947). "The Magnetic Electron Microscope Objective: Contour Phenomena and the Attainment of High Resolving Power". Journal of Applied Physics. 18 (1): 48. doi:10.1063/1.1697554. ISSN 0021-8979.
7. Anjam Khursheed (2011). Scanning Electron Microscope Optics and Spectrometers. World Scientific. ISBN 978-981-283-667-0.
8. Peter W. Hawkes; E. Kasper (24 April 1996). Principles of Electron Optics: Basic Geometrical Optics. Academic Press. pp. 517–. ISBN 978-0-08-096241-2.
9. Riecke, W.D. (11 November 2013). Magnetic Electron Lenses. Springer Science & Business Media. p. 269. ISBN 978-3-642-81516-4.
10. P. Rai-Choudhury (January 1997). Handbook of Microlithography, Micromachining, and Microfabrication: Microlithography. IET. p. 154. ISBN 978-0-85296-906-9.
11. Peter W. Hawkes (6 November 2013). The Beginnings of Electron Microscopy. Elsevier Science. p. 369. ISBN 978-1-4832-8465-1.
12. Saul Wischnitzer (22 October 2013). Introduction to Electron Microscopy. Elsevier Science. pp. 91–92. ISBN 978-1-4831-4869-4.
13. Rudnaya, M.E.; Van den Broek, W.; Doornbos, R.M.P.; Mattheij, R.M.M.; Maubach, J.M.L. (2011). "Defocus and twofold astigmatism correction in HAADF-STEM". Ultramicroscopy. 111 (8): 1043–1054. doi:10.1016/j.ultramic.2011.01.034. ISSN 0304-3991. PMID 21740867.
14. B.G. Yacobi; L.L. Kazmerski; D.B. Holt (29 June 2013). Microanalysis of Solids. Springer Science & Business Media. p. 81. ISBN 978-1-4899-1492-7.
15. Bischoff, M., Henstra, A., Luecken, U., & Tiemeijer, P. C. (2013). U.S. Patent No. 8,569,693. Washington, DC: U.S. Patent and Trademark Office.