725
length) causes the beam to converge to focus before the elec-
trons reach the surface of the sample. Since the electrons then
begin to diverge from this crossover point, the beam has
broadened beyond its narrowest waist and is wider than opti-
mal when it strikes the surface of the sample, thus producing
an out-of-focus image. Conversely, the right-hand portion of. Fig. 5.5 shows the beam behavior in an underfocused con-
dition. Here the magnetic field is too weak, and the beam is
not fully brought to crossover before it strikes the surface of
the sample, and again the beam diameter is broader than
optimal, resulting in an out-of-focus image.
Using these schematics as a guide, it is easier to under-
stand what is happening electron optically when the SEM
user focuses the image. Changes in the focus control result
in changes in the electrical current in the objective lens,
which results in raising or lowering the crossover of the elec-
tron beam relative to the surface of the sample. The distance
between the objective lens exit aperture and this beam cross-
over point is displayed on the microscope as the working
distance, W. On most microscopes you can see the working
distance change numerically on the screen as you make
gross changes in the focus setting, reflecting this vertical
motion of the beam crossover in the SEM chamber. It is
important to note that the term working distance is also used
by some microscopists when referring to the distance
between the objective lens pole piece and the surface of the
sample. The value of W displayed on the microscope will
accurately reflect this lens-to-sample distance if the sample
is in focus.
Astigmatism
The pointy cones drawn in. Fig. 5.5 are a useful fiction for
representing the large-scale behavior of a focused electron
beam, but if we consider the beam shape carefully near the
beam crossover point this conical model of the beam breaks
down.. Figure 5.6 is a more realistic picture of the beam
shape as it converges to its narrowest point and then begins
to diverge again below that plane. For a variety of reasons,
mostly the effects of lens aberrations and other imperfec-
tions, even at its narrowest point the beam retains a finite
beam diameter. In other words, it can never be focused to a
perfect geometrical point. The left side of. Fig. 5.6 shows the
beam narrowing gently but never reaching a sharp point,
reflecting this reality. Ideally, cross sections through the beam
at different heights will all be circles, as shown in the right of. Fig. 5.6. If the beam is underfocused or overfocused, as
shown in. Fig. 5.5, the consequence is a blurry image caused
by the larger-diameter beam (larger blue circles in. Fig. 5.6
above and below the narrowest point).
In real SEMs the magnetic fields created in the electron
optics are never perfectly symmetric. Although the
manufacturers strive for ideal circular symmetry in round
lenses, invariably there are defects in the lens yoke, the elec-
trical windings, the machining of the pole pieces, or other
problems that lead to asymmetries in the lens field and ulti-
mately to distortions in the electron beam. Dirt or contami-
nation buildup on the apertures in the microscope can also
be an important source of distorted beam shapes. Since the
dirt on the aperture is electrically non-conductive, it can
. Fig. 5.5 Schematic of the
conical electron beam as it strikes
the surface of the sample, show-
ing overfocus (left), correct focus
(center), and underfocus (right).
From this view it is clear that if
the beam converges to crossover
above the surface of the sample
(left) or below the surface (right),
the beam diameter is wider at the
sample than the diameter of an
in-focus beam (center)
Chapter 5 · Scanning Electron Microscope (SEM) Instrumentation