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

88 Chapter 3
A related concept is depth of field: the distance �u (along the optic axis)
that the specimen can be moved without its image (focused at a given plane)
becoming noticeably blurred. Replacing the TEM imaging system with a
single lens of fixed focal length f and using 1/u + 1/v = 1/f , the change in
image distance is �v = � (v/u) 2 �u = � M 2 �u (the minus sign denotes a
decrease in v, as in Fig. 3-15b). The radius of the disk of confusion in the
image plane (due to defocus) is R = ���v� = (�/M) (��v) = � M �u,
equivalent to a radius �r = R/M = ��u at the specimen plane. This same
result can be obtained more directly by extrapolating backwards the solid ray
in Fig. 3-15b to show that the electrons that arrive at a single on-axis point in
the image could have come from anywhere within a circle whose radius
(from geometry of the topmost right-angle triangle) is �r = ��u.
If we take � = 5 mrad and set the loss or resolution �r equal to the TEM
resolution (� 0.2 nm), we get �u = (0.2 nm)/(0.005) = 40 nm as the depth of
field. Most TEM specimens are of the order 100 nm or less in thickness. If
the objective lens is focused on features at the mid-plane of the specimen,
features close to the top and bottom surfaces will still be acceptably in focus.
In other words, the small value of � ensures that a TEM image is normally a
projection of all structure present in the specimen. It is therefore difficult or
impossible to obtain depth information from a single TEM image. On the
other hand, this substantial depth of field avoids the need to focus on several
different planes within the specimen, as is sometimes necessary in a lightoptical
microscope where � may be large and the depth of field can be
considerably less than the specimen thickness.
3.6 Vacuum System
It is essential to remove most of the air from the inside of a TEM column, so
that the accelerated electrons can follow the principles of electron optics,
rather than being scattered by gas molecules. In addition, the electron gun
requires a sufficiently good vacuum in order to prevent a high-voltage
discharge and to avoid oxidation of the electron-emitting surface.
A mechanical rotary pump (RP) is used in many vacuum systems. This
pump contains a rotating assembly, driven by an electric motor and equipped
with internal vanes (A and B in Fig. 3-16) separated by a coil spring so that
they press against the inside cylindrical wall of the pump, forming an airtight
seal. The interior of the pump is lubricated with a special oil (of low vapor
pressure) to reduce friction and wear of the sliding surfaces. The rotation
axis is offset from the axis of the cylinder so that, as gas is drawn from the
inlet tube (at A in Fig. 3-16a), it expands considerably in volume before
being sealed off by the opposite vane (B in Fig. 3-16b).