2.1 Energy-Analyzing and Energy-Selecting Systems 39
The Wien filter is generally used with decelerated electrons. In other words, the
filter is operated at a potential −V
0
+ V
1
which is close to the negative potential
−V
0
of the electron source. The positive bias V
1
is obtained from a power supply
connected to the high-voltage line; its value, typically in the range 100–1000 eV,
determines the energy (eV
1
) of the electrons that can move in a straight line through
the filter. The retarding and accelerating fields at the entrance and exit of the filter
act as electrostatic lenses (Fig. 2.5), whose effect must be taken into account in the
design of the system.
Although retardation involves the inconvenience of handling high voltages, it
provides several advantages. First of all, the dispersion at the chromatic focus is
increased by a factor V
0
/V
1
for a given length L of the filter; values of 100 μm/eV or
more are typical. The electrostatic lens at the exit of the filter can be used to project
the spectrum onto the detection plane, with either a decrease or a further increase in
the dispersion, depending on the distance of the final image. Second, the required
magnitudes and stabilities of B and E are reduced and the mechanical tolerances of
the polepieces and electrodes are relaxed. Third, because the electron velocity for
straight-line transmission depends on V
1
rather than V
0
, fluctuations and drift in V
0
do not affect the energy resolution. This factor is particularly important where high
resolution must be combined with long recording times, for example, when record-
ing inner-shell losses using a field-emission STEM (Batson, 1985). A Wien filter
used in conjunction with a monochromator (Section 2.1.4) achieved an energy reso-
lution of 5 meV for 30-keV electrons (Geiger et al., 1970), yielding spectra showing
vibrational and phonon modes of energy loss (Fig. 1.9). These vibrational modes
can be studied by infrared absorption spectroscopy but EELS offers the potential of
much better spatial resolution.
Because the system just discussed does not focus in the y-direction, the energy-
loss spectrum is produced as a function of distance along a straight line in the
entrance plane, this line being defined by an entrance slit. If a diffraction pattern
(or a magnified image) of the s pecimen is projected onto the slit plane, using the
lenses of a CTEM, the final image will contain a map of electron intensity as
a function of both energy loss and scattering angle (or specimen coordinate). A
two-dimensional sensor placed at the final-image plane can therefore record a large
amount of information about the specimen (Batson and Silcox, 1983).
The Wien filter can become double focusing if either E or B is made nonuni-
form, for example, by curving the electric field electrodes, by tilting t he magnetic
polepieces to create a magnetic field gradient, or by shaping both the electric and
magnetic fields to provide a quadrupole action (Andersen, 1967). The device is then
suitable for use as an imaging filter in a fixed-beam TEM (Andersen and Kramer,
1972). Aberrations of the filter can be corrected by introducing multipole elements
(Andersen, 1967; Martinez and Tsuno, 2008).
2.1.4 Electron Monochromators
Besides being dependent on the spectrometer, the energy resolution of an energy
analysis system is limited by energy spread in the electron beam incident on