Physical Principles of Electron Microscopy: An Introduction to TEM ...

34 Chapter 2
2.3. Imaging with Electrons
Electron optics has much in common with light optics. We can imagine
individual electrons leaving an object and being focused into an image,
analogous to visible-light photons. As a result of this analogy, each electron
trajectory is often referred to as a ray path.
To obtain the equivalent of a convex lens for electrons, we must arrange
for the amount of deflection to increase with increasing deviation of the
electron ray from the optic axis. For such focusing, we cannot rely on
refraction by a material such as glass, as electrons are strongly scattered and
absorbed soon after entering a solid. Instead, we take advantage of the fact
that the electron has an electrostatic charge and is therefore deflected by an
electric field. Alternatively, we can use the fact that the electrons in a beam
are moving; the beam is therefore equivalent to an electric current in a wire,
and can be deflected by an applied magnetic field.
Electrostatic lenses
The most straightforward example of an electric field is the uniform field
produced between two parallel conducting plates. An electron entering such
a field would experience a constant force, regardless of its trajectory (ray
path). This arrangement is suitable for deflecting an electron beam, as in a
cathode-ray tube, but not for focusing.
The simplest electrostatic lens consists of a circular conducting electrode
(disk or tube) connected to a negative potential and containing a circular
hole (aperture) centered about the optic axis. An electron passing along the
optic axis is repelled equally from all points on the electrode and therefore
suffers no deflection, whereas an off-axis electron is repelled by the negative
charge that lies closest to it and is therefore deflected back toward the axis,
as in Fig. 2-6. To a first approximation, the deflection angle is proportional
to displacement from the optic axis and a point source of electrons is focused
to a single image point.
A practical form of electrostatic lens (known as a unipotential or einzel
lens, because electrons enter and leave it at the same potential) uses
additional electrodes placed before and after, to limit the extent of the
electric field produced by the central electrode, as illustrated in Fig. 2-5.
Note that the electrodes, and therefore the electric fields which give rise to
the focusing, have cylindrical or axial symmetry, which ensures that the
focusing force depends only on radial distance of an electron from the axis
and is independent of its azimuthal direction around the axis.