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.
aplanat; chromatic aberration; correction of aberrations; eikonal method; energy filter; hexapole corrector; mirror corrector; spherical aberration; ultracorrector.
The information cube consisting of an energy-loss spectrum for each image point.
, κ x of the design curve and coordinates y x, y and z.
Path of the electron as orthogonal trajectories of the set of surfaces of constant reduced action in the case
Illustration of the theorem of alternating images.
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.
Arrangement of the elements of a spherical-aberration corrector, which does not introduce any second-order aberrations outside of the system (© 2002 Springer ).
Course of the second-order fundamental rays
u 11, u 12 and u 22 within the hexapole corrector shown in figure 6 (© 2002 Springer ).
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 ).
Coma-free arrangement of the objective lens and the hexapole corrector by means of a telescopic transfer doublet (© 2002 Springer ).
Course of the secondary fundamental rays within the planator shown in figure 8 in the case that the sextupoles
S 2 and S 4= S 2 are not excited (© 2002 Springer ).
Arrangement and strengths of the quadrupoles, and course of the fundamental rays within the first septuplet of the ultracorrector.
Course of the fundamental axial rays
x α, y β and the field rays x γ, y δ within the ultracorrector.
Course of the pseudo fundamental rays
and locations of the octopoles
, ν=1, …, 19, within the ultracorrector.
x, y, h) of an electron with respect to the location (0, 0, ζ) of the corresponding reference electron.
Sectional view and equipotentials of a diode mirror with bore radius
r in the case Φ =-0.25 Φ m . The circular edges of the electrode surfaces have a radius of 0.4 c r. The equipotentials are labeled in units of the column potential Φ . c
Paths of the reference electron ζ, of the fundamental rays
u μ, u ξ and of the axial deviations h σ and h ν as functions of τ. The optic axis intersects the surface of the mirror electrode at the origin of the coordinate system.
Paths of the fundamental rays
u μ, u ξ and of the axial deviations h σ and h ν as functions of ζ. The slope of u ξ and h ν diverges at the turning point ζ =0.865431 T r. The ray u μ intersects the optic axis at ζ =7.73760 m r.
Sectional view of a tetrode mirror. The potentials Φ
, Φ m 1 and Φ 2 determine the focal length, the chromatic aberration and the spherical aberration.
Variation range of the tetrode mirror shown in figure 18. The coefficient of the chromatic aberration
and that of the spherical aberration
can be adjusted within the shaded area, while the Gaussian image plane remains fixed at a distance of 210 mm from the mirror electrode.
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 ).
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.
View of the toroidal deflection elements and the dispersive properties of the electrostatic monochromator.
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.
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 ).
Arrangement of the bending magnets and the sextupoles for the corrected 90° W-filter operating in the type I mode (© 2002 Springer ).
Course of the fundamental paraxial rays along the
straightened axis of the first half of the W-filter depicted in figure 25 (© 2002 Springer ).
Oscillating path of the dispersion ray
x κ along the straightened optic axis of the W-filter shown in figure 25 (© 2002 Springer ).
Arrangement of the conical bending magnets for the highly dispersive 115° W-filter operating in the type II mode (© 2002 Springer ).
Course of the fundamental paraxial rays along the straightened optic axis of the type II W-filter shown in figure 14 (© 2002 Springer ).
Path of the dispersion ray
x κ within the 115° W-filter (© 2002 Springer ).
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 ).
Scheme of the SESAM 2000 illustrating the arrangement of the constituent elements.
All figures (32)
Design for an aberration corrected scanning electron microscope using miniature electron mirrors.
Ultramicroscopy. 2018 Jun;189:1-23. doi: 10.1016/j.ultramic.2018.03.009. Epub 2018 Mar 7.
The objective lens of the electron microscope with correction of spherical and axial chromatic aberrations.
Microscopy (Oxf). 2017 Oct 1;66(5):356-365. doi: 10.1093/jmicro/dfx023.
Microscopy (Oxf). 2017.
Prospects for aberration-free electron microscopy.
Ultramicroscopy. 2005 Apr;103(1):1-6. doi: 10.1016/j.ultramic.2004.11.017. Epub 2005 Jan 19.
Electrostatic correction of the chromatic and of the spherical aberration of charged-particle lenses (part II).
J Electron Microsc (Tokyo). 2002;51(1):45-51. doi: 10.1093/jmicro/51.1.45.
J Electron Microsc (Tokyo). 2002.
Present status and future prospects of spherical aberration corrected TEM/STEM for study of nanomaterials
Sci Technol Adv Mater. 2008 Jun 2;9(1):014111. doi: 10.1088/1468-6996/9/1/014111. eCollection 2008 Jan.
Sci Technol Adv Mater. 2008.
27877937 Free PMC article.
Origin of large plasticity and multiscale effects in iron-based metallic glasses.
Nat Commun. 2018 Apr 6;9(1):1333. doi: 10.1038/s41467-018-03744-5.
Nat Commun. 2018.
29626189 Free PMC article.
A novel low energy electron microscope for DNA sequencing and surface analysis.
Ultramicroscopy. 2014 Oct;145:36-49. doi: 10.1016/j.ultramic.2014.01.007. Epub 2014 Jan 31.
24524867 Free PMC article.
Progress toward an aberration-corrected low energy electron microscope for DNA sequencing and surface analysis.
J Vac Sci Technol B Nanotechnol Microelectron. 2012 Nov;30(6):6F402. doi: 10.1116/1.4764095. Epub 2012 Oct 26.
J Vac Sci Technol B Nanotechnol Microelectron. 2012.
23847748 Free PMC article.
A monochromatic, aberration-corrected, dual-beam low energy electron microscope.
Ultramicroscopy. 2013 Jul;130:13-28. doi: 10.1016/j.ultramic.2013.02.018. Epub 2013 Mar 21.
23582636 Free PMC article.
The three-dimensional point spread function of aberration-corrected scanning transmission electron microscopy.
Microsc Microanal. 2011 Oct;17(5):817-26. doi: 10.1017/S1431927611011913. Epub 2011 Aug 31.
Microsc Microanal. 2011.
21878149 Free PMC article.