Status Quo
Introduction
One of the experimental setups, at which circular
dichroism can be measured, is realized when a suitable specimen
is illuminated by a system of interference fringes with a spacing
adapted to the object structure and with a controllable position
of the fringes. This is achieved by means of two overlapping coherent
electron beams, where the mutual angle of propagation and mutual
phase shift has to be controlled. Such an illumination of the
specimen can be achieved by placing a biprism into a condenser
system of the microscope.
The Möllenstedttype biprism [1] is analogous
to the optical biprism (Fig. 1). It consists of a positively biased
thin filament (diameter less than a micrometer) placed between
two grounded plates. The electric field around the filament deflects
the electron waves, so that they interfere below the biprism.
The ingenuity of the biprism is that the deflection angle is independent
of the distance of the electrons from the filament and that the
biprism has virtually no aberrations. The deflection angle is
proportional to the voltage Ubp between the filament and the plates
,
(1)
with the deflection coefficient dependent on
biprism dimensions.
Fig. 1 Principle of biprism operation.
The important parameters of an interference pattern are fringe
spacing S, interference width W, and fringe contrast V (Fig. 2).
The contrast is defined as
,
(2)
where Imax is the maximum and Imin the minimum
intensity of the interference fringes.
Fig. 2 Latex spheres and gold nanocrystals on a holy carbon foil
illuminated with two interfering electron beams.
Fringe spacing, interference width and fringe
contrast can be controlled by the distance a of the crossover
from the biprism, by the distance b of the image plane from the
biprism, and by the biprism voltage Ubp [2] (Fig. 3).
,
(3)
,
(4)
,
(5)
where rf is the filament radius, r0 is the effective
radius of the emitting area in the electron source, and is the
wavelength.
Fig. 3 Geometric construction of virtual sources S1, S2, which
arise due to beam splitting by the biprism.
The biprism is placed in the condenser system,
which consists of 4 lenses (Fig. 4). By adjusting focal length
of the lenses (through varying current in the lenses) and biprism
voltage one can (hopefully) adjust S, W, V so that the measurement
of circular dichroism is possible.
Fig. 4 Scheme of the condenser system.
Although we have a lot of experience with the
biprism mounted below the objective lens for holographic measurements
[2], we presently have only few experiences with a biprism in
the illumination system. We have found several problems that we
describe further in the following.
Biprism Holder
The standard biprism holder, which is designed
to be mounted in the first intermediate image plane (below the
objective lens), is too big for the Condenser2 port of the microscope
(above the objective lens)  Fig 5. A downscaled copy of the
standard holder that would fit in a C2 port is hardly manufacturable.
Therefore we developed a new construction (Figs. 6  8), which
can be manufactured in smaller dimensions, and which is in addition
more resistant against flashovers [3].
Fig. 5 Comparison of dimensions of a standard
C2 aperture holder (top) and standard biprism holder (bottom).
Fig. 6 Comparison of old (left) and new (right)
biprism holder construction.
Old construction. The biprism is soldered by means of a silver
paste on 2 rivets glued into insulation cylinders. The holes in
the holder, necessary for the isolation, weaken the stiffness
of the holder, which is only 1 mm thick at the biprism. Each rivet
is contacted at the bottom of the holder with a thin wire. The
wires are glued in the grooves. Flashovers often happen at the
contact points between the wires and the rivets.
New construction. Assembling the new construction: (1) A Ushaped
electrode is glued in a supporting stand in the form of a rectangular
block with two holes parallel to the axis of the holder. (2) The
supporting stand is fastened with a screw to the holder head.
The electrode is contacted in one point only with a silver paste
at the crook of the 'U'. (3) The biprism is attached to the Ushaped
electrode with a silver paste.
Fig. 7 Technical drawing of the improved biprism
holder.
Fig. 8 Photograph of the improved biprism holder.
Introduction into Function of Electromagnetic Lenses
The C2 port of the microscope is placed in
the middle of the Condenser 2 lens, i.e. the biprism is placed
inside the lens. Since there is no corresponding theory of such
a system reported in the literature, imaging properties of a biprism
in a lens were calculated [4]<link1>. The conclusion of
the calculations is: In an approximation valid for thin lenses
and a thin biprism, the system biprisminsidealens is optically
equivalent to the system biprismjustbehindthelens. In order
to better understand the electron optics two programs <link2><link3>
were written for live visualization of electron trajectories in
a lens and in the system of lenses while varying the parameters
of the lenses or of the beam (Fig. 9, 10).
Fig. 9 Screenshot of program visualising beam
paths in an electromagnetic lens with a builtin biprism.
Fig. 10 Screenshot of program visualising beam
paths in a condenser system.
Exploring Possible Setups
After insertion of the biprism in the C2 port
of the microscope and applying a voltage to it, interference fringes
with spacings of 5 nm to 40 nm are observable [3]. However, for
the measurement of the dichroic signal, fringe spacings of either
~ 0.1 nm or ~ 200 nm are necessary. This could, in principle,
be achieved by a corresponding setup of the condenser system,
i.e. by deflection angle of the biprism (controlled by the voltage
on the biprism), by focal lengths of the Condenser 1, Condenser
2 and Minicondenser lenses (controlled by currents through the
lenses), as well as by axially moving the first image of the electron
gun  "the crossover" (controlled by gun lens voltage
and extraction voltage). This means optimizing 6 parameters is
needed.
Even though we put a large effort to reach
the desirable fringe spacing by varying various microscope parameters,
we did not succeed to reach the necessary fringe spacing. It turned
out that the condenser system is so complicate that it cannot
be adjusted intuitively. We used a model of the system within
thin lens approximation (provided by FEI Company), which enabled
us to explore all possible setups by brute force method  i.e.
just by varying all possible parameters. The result of the simulations
and experiments are summarized in Fig. 11. It shows that desired
fringe spacing is not achievable in a highresolution mode of
the microscope. The graph in Fig. 11 should be understood as follows.
The width of the interference field W is a
linear function of the biprism voltage Ubp (Cf. Eq. 3):
,
(6)
and the fringe spacing S is indirectly proportional
to the biprism voltage (Cf. Eq. 4):
,
(7)
These two relationships can be plotted in a
WS diagram (Fig. 11) by the means of a set of parametric curves,
the parameter of which is the biprism voltage. The position of
a curve is given by the constants A, B, C, which in turn depend
on the actual configuration of the condenser system (position
of the crossover, excitation of the condenser lenses). By trying
all possible combinations of the adjustable parameters, the curve
moves in the diagram, filling an area that defines accessible
fringe spacings S and interference widths W.
The dashed red line in Fig. 11 marks fringe
spacings and interference widths achievable with a standard objective
lens (SuperTwin lens) and a biprism placed in the second condenser
aperture (C2aperture). It is obvious that this configuration
does not allow reaching the desirable fringe spacings. The achievable
area would move rightupwards (overlapping the area for the CHIRALTEM),
if the biprism were placed in the first condenser aperture (C1aperture).
Since the C1aperture is placed in the ultrahighvacuum part
of the microscope, any changes must be done by a service engineer.
But finally, we found that switching the objective
lens off (Low Magnification mode) is a way to approach the desired
fringe spacing of ~ 200 nm  the area marked by the blue dotted
line in Fig. 11. Optionally, one can use the Lorentz objective
lens [6], to win back the degree of freedom that was lost by switching
the objective lens off. An image of 200 nm fringes is displayed
in Fig. 12.
Fig. 11 Interference width W vs. fringe spacing S in specimen
plane in a FEI CM200 series microscope for different excitations
of the C2 lens. Curves with symbols show experimental data (Extraction
voltage 3.81kV, gun lens 3, spot size 3, excitation of second
condenser lens C2 given in % of maximal lens current), the lines
are calculations within thin lens model. The dashed red line marks
an envelope of curves for possible microscope configurations achievable
with a SuperTwin lens and a biprism in the second condenser aperture.
Similarly, the dotted blue line marks the area accessible with
a Lorentz lens. The orange parallelogram denotes the area suitable
for CHIRALTEM. The forbidden area is defined by S < W, i.e.
less than one fringe in the interference field.
Fig. 12 Latex spheres of diameter 204 nm on
a carbon foil illuminated by two interfering beams with a fringe
spacing of about 200 nm.
Acknowledgements
We would like to express our gratitude to Dr.
Peter Tiemeijer from FEI Company for providing the information
necessary to progress the project.
References
[1] G. Möllenstedt, H. Düker, "Fresnelscher
Interferenzversuch mit einem Biprisma für Elektronenwellen",
Zeitschr. für Physik 42 (1955) 41
[2] M. Lehmann, H. Lichte, "Tutorial on
Offaxis Electron Holography", Microscopy and Microanalysis
8 (2002) 447
[3] P. Formanek, B. Einenkel, H. Lichte, "An
improved construction of electron biprism holder for the C2aperture"
Proc. Microscopy Conference MC2005, Davos, Switzerland, p. 30
[4] <link1>
[5] P. Formanek, B. Einenkel, H. Lichte, "Biprism
in condenser system for coherent twobeam illumination of an object",
Proc. Microscopy Conference MC2005, Davos, Switzerland, p. 31
[6] J. Zweck, B. Bormans, "The CM30 Lorentz
Lens", Philips Electron Optics Bulletin 132 (1992) 1
