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Review
, 9 (1), 014107
eCollection

Optics of High-Performance Electron Microscopes

Affiliations
Review

Optics of High-Performance Electron Microscopes

H H Rose. Sci Technol Adv Mater.

Abstract

During recent years, the theory of charged particle optics together with advances in fabrication tolerances and experimental techniques has lead to very significant advances in high-performance electron microscopes. Here, we will describe which theoretical tools, inventions and designs have driven this development. We cover the basic theory of higher-order electron optics and of image formation in electron microscopes. This leads to a description of different methods to correct aberrations by multipole fields and to a discussion of the most advanced design that take advantage of these techniques. The theory of electron mirrors is developed and it is shown how this can be used to correct aberrations and to design energy filters. Finally, different types of energy filters are described.

Keywords: aplanat; chromatic aberration; correction of aberrations; eikonal method; energy filter; hexapole corrector; mirror corrector; spherical aberration; ultracorrector.

Figures

Figure 1
Figure 1
The information cube consisting of an energy-loss spectrum for each image point.
Figure 2
Figure 2
Curvatures κx, κy of the design curve and coordinates x, y and z.
Figure 3
Figure 3
Path of the electron as orthogonal trajectories of the set of surfaces of constant reduced action in the case formula image .
Figure 4
Figure 4
Illustration of the theorem of alternating images.
Figure 5
Figure 5
Scheme of the path of the fundamental paraxial trajectories and location of the images and heam-limiting apertures in a transmission electron microscope illustrating the theorem of alternating images.
Figure 6
Figure 6
Arrangement of the elements of a spherical-aberration corrector, which does not introduce any second-order aberrations outside of the system (© 2002 Springer [34]).
Figure 7
Figure 7
Course of the second-order fundamental rays u11, u12 and u22 within the hexapole corrector shown in figure 6 (© 2002 Springer [34]).
Figure 8
Figure 8
Hexapole planator compensating for the third-order image curvature and field astigmatism. The planator also introduces a negative spherical aberration, which depends on the coefficients of the field aberrations prior to their correction (© 2002 Springer [34]).
Figure 9
Figure 9
Coma-free arrangement of the objective lens and the hexapole corrector by means of a telescopic transfer doublet (© 2002 Springer [34]).
Figure 10
Figure 10
Course of the secondary fundamental rays within the planator shown in figure 8 in the case that the sextupoles S2 and S4=S2 are not excited (© 2002 Springer [34]).
Figure 11
Figure 11
Arrangement and strengths of the quadrupoles, and course of the fundamental rays within the first septuplet of the ultracorrector.
Figure 12
Figure 12
Course of the fundamental axial rays xα, yβ and the field rays xγ, yδ within the ultracorrector.
Figure 13
Figure 13
Course of the pseudo fundamental rays uω, formula image , uη and formula image and locations of the octopoles Oν, ν=1, …, 19, within the ultracorrector.
Figure 14
Figure 14
Position (x, y, h) of an electron with respect to the location (0, 0, ζ) of the corresponding reference electron.
Figure 15
Figure 15
Sectional view and equipotentials of a diode mirror with bore radius r in the case Φm=-0.25 Φc. The circular edges of the electrode surfaces have a radius of 0.4 r. The equipotentials are labeled in units of the column potential Φc.
Figure 16
Figure 16
Paths of the reference electron ζ, of the fundamental rays uμ, uξ and of the axial deviations hσ and hν as functions of τ. The optic axis intersects the surface of the mirror electrode at the origin of the coordinate system.
Figure 17
Figure 17
Paths of the fundamental rays uμ, uξ and of the axial deviations hσ and hν as functions of ζ. The slope of uξ and hν diverges at the turning point ζT=0.865431 r. The ray uμ intersects the optic axis at ζm=7.73760 r.
Figure 18
Figure 18
Sectional view of a tetrode mirror. The potentials Φm, Φ1 and Φ2 determine the focal length, the chromatic aberration and the spherical aberration.
Figure 19
Figure 19
Variation range of the tetrode mirror shown in figure 18. The coefficient of the chromatic aberration Rωκ and that of the spherical aberration formula image can be adjusted within the shaded area, while the Gaussian image plane remains fixed at a distance of 210 mm from the mirror electrode.
Figure 20
Figure 20
Scheme of a corrected system. The tetrode mirror is implemented via a dispersion-free magnetic beam separator. The thin shaded regions indicate the induction coils, which are placed at the surface of the pole plates (© 2002 Springer [34]).
Figure 21
Figure 21
Horizontal xz cross-section through the omega-shaped electrostatic monochromator and course of the fundamental rays along the straightened optic axis within the horizontal and the vertical sections.
Figure 22
Figure 22
View of the toroidal deflection elements and the dispersive properties of the electrostatic monochromator.
Figure 23
Figure 23
Schematic arrangement of the deflection elements and the sextupoles within the MANDOLINE filter, the distance between the energy selection plane and the diffraction image in front of the filter defines the lengthening of the column.
Figure 24
Figure 24
Geometry of a conical bending magnet producing homogeneous dipole and quadrupole fields along the circular axis in the region between the tapered poles (© 2002 Springer [34]).
Figure 25
Figure 25
Arrangement of the bending magnets and the sextupoles for the corrected 90° W-filter operating in the type I mode (© 2002 Springer [34]).
Figure 26
Figure 26
Course of the fundamental paraxial rays along the straightened axis of the first half of the W-filter depicted in figure 25 (© 2002 Springer [34]).
Figure 27
Figure 27
Oscillating path of the dispersion ray xκ along the straightened optic axis of the W-filter shown in figure 25 (© 2002 Springer [34]).
Figure 28
Figure 28
Arrangement of the conical bending magnets for the highly dispersive 115° W-filter operating in the type II mode (© 2002 Springer [34]).
Figure 29
Figure 29
Course of the fundamental paraxial rays along the straightened optic axis of the type II W-filter shown in figure 14 (© 2002 Springer [34]).
Figure 30
Figure 30
Path of the dispersion ray xκ within the 115° W-filter (© 2002 Springer [34]).
Figure 31
Figure 31
Arrangement of the doubly symmetric W-filter in the case that the inclination angles of the tapered pole pieces coincide for all magnets (© 2002 Springer [34]).
Figure 32
Figure 32
Scheme of the SESAM 2000 illustrating the arrangement of the constituent elements.

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