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

72 Chapter 3
The second condenser (C2) lens is a weak magnetic lens (f � several
centimeters) that provides little or no magnification ( M � 1) but allows the
diameter of illumination (d) at the specimen to be varied continuously over a
wide range. The C2 lens also contains the condenser aperture (the hole in
the condenser diaphragm) whose diameter D can be changed in order to
control the convergence semi-angle � of the illumination, the maximum
angle by which the incident electrons deviate from the optic axis.
The case of fully-focused illumination is shown in Fig. 3-8a. An image
of the electron source is formed at the specimen plane (image distance v0),
and the illumination diameter at that plane is therefore d0 = M d1 (� d1 if
object distance u � v0). This condition provides the smallest illumination
diameter (below 1 �m), as required for high-magnification imaging. Because
the condenser aperture is located close to the principal plane of the lens, the
illumination convergence angle is given by 2�0 � D/v0 � 10 -3 rad = 1 mrad
for D = 100 �m and v0 = 10 cm.
Figure 3-8b shows the case of underfocused illumination, in which the
C2 lens current has been decreased so that an image of the electron source is
formed below the specimen, at a larger distance v from the lens. Because the
specimen plane no longer contains an image of the electron source, the
diameter of illumination at that plane is no longer determined by the source
diameter but by the value of v. Taking v = 2v0, for example, simple geometry
gives the convergence semi-angle at the image as ��D/v ��0/2 and the
illumination diameter as d � (2�)(v � v0) ��0v0 = 50 �m. As shown by the
dashed lines in Fig. 3-8b, electrons arriving at the center of the specimen at
the previous angle �0 relative to the optic axis (as in Fig. 3-8a) would have
to originate from a region outside the demagnified source, and because there
are no such electrons, the new convergence angle � of the illumination must
be smaller than �0. Using the brightness-conservation theorem, Eq. (3.4), the
product (�d) must be the same at the new image plane and at the specimen,
giving � = �0 (d0/d) � (0.5mrad)(1�m/50�m) � 0.010 mrad. Defocusing the
illumination therefore ensures that the incident electrons form an almost
parallel beam. This condition is useful for recording electron-diffraction
patterns in the TEM or for maximizing the contrast in images of crystalline
specimens and is obtained by defocusing the C2 lens or using a small C2
aperture,
or both.
The situation for overfocused illumination, where the C2 current has
been increased so that the image occurs above the specimen plane, is shown
in Fig. 3-8c. In comparison with the fully-focused condition, the illumination
diameter d is again increased and the convergence semi-angle � at the
specimen plane is reduced in the same proportion, in accordance with the
brightness theorem. Note that this low convergence angle occurs despite an