73 5
accumulate an electric charge when the beam electrons strike
it, and the resulting electrostatic fields can warp and bend the
beam into odd and complex shapes that no longer have a cir-
cular cross section.
By far the most important of these distortions is called
two-fold astigmatism, which in practice is often referred to
just as astigmatism. In this specific distortion the magnetic
field that focuses the electrons is stronger in one direction
than in the orthogonal direction, resulting in a beam with an
elliptical cross section instead of a circular one. In beams
exhibiting astigmatism the electrons come to closest focus in
the x-direction at a different height than the y-direction, con-
sistent with the formation of elliptical cross sections. These
effects are shown schematically in. Fig. 5.7. Similar to
. Fig. 5.6, the focused beam is shown in perspective on the
left side of the diagram, while a series of cross sections of the
beam are shown on the right of the figure. In the case shown
here, as the beam moves down the optical axis of the SEM, the
cross section changes from an elongated ellipse with long axis
in the y-direction, to a circle (albeit with a larger diameter
than the equivalent circle in. Fig. 5.6), and then to another
elongated ellipse, but this time with its long axis oriented in
the x-direction. This progression from a near-line-focus to a
broader circular focus and then to a near-line-focus in an
orthogonal direction is the hallmark of a beam exhibiting
astigmatism.
This behavior is also easily visible in the images produced
by rastering the beam on a sample. When the beam cross sec-
tion is highly elongated at the surface of the sample, the
image resolution is degraded badly in one direction, produc-
ing a blurring effect with pronounced linear asymmetry. It
appears as if the image detail is sheared or stretched in one
direction but not the other. If the focus knob is adjusted when
the beam is astigmatic, a point can be reached when this
image shearing or linear asymmetry is eliminated or at least
greatly reduced. This is the best focus obtainable without. Fig. 5.6 Perspective view of the electron beam as it converges to
focus and subsequently diverges (left), and a series of cross-sectional
areas from the same beam as it travels along the optic axis (right). Note
that although this beam does not exhibit any astigmatism it still does
not focus to a point at its narrowest waist
. Fig. 5.7 Perspective view of an astigmatic electron beam as it con-
verges to focus and subsequently diverges (left), and a series of cross-
sectional areas from the same beam as it travels along the optic axis
(right). Because this beam exhibits significant astigmatism, the cross
sections are not circular and their major axis changes direction after
passing through focus
5.2 · Electron Optical Parameters