Diplomarbeit Diplom-Ingenieur - Institut für Halbleiter

16
There are two important, adjustable apertures between the objective and
intermediate lens. The first is the objective aperture, which is located at the level of
the focal plane and allows the selection of electrons from distinct scattered beams for
image formation. The other is placed in the image plane of the objective lens and acts
as a virtual aperture to choose the area of interest on the sample. It is called field-
limiting aperture or selected area diffraction aperture (SAD).
The JEOL JEM 2011 FastTem uses a LaB6 filament as electron source and the
electrons can be accelerated up to 200keV between the Wehnelt cylinder and the
anode plates. Electrons with an energy of 200keV are in the range where relativistic
effects are playing a role. This leads to a wavelength of the particles of 2.5·10 -2 Å.
The microscope is an electron system, thus the theoretical diffraction limit is given by
the Rayleigh criterion (eqn. 3.1) [32].
The denominator of equation 3.1 is called the numerical aperture and is the product of
the diffraction-index and sin β, whereas β is the semiangle of collection. λ refers to
the wavelength of the electrons. For an electron energy of 200keV this wavelength is
2.5·10 -2 Å. The maximum resolution (the numerical aperture is set to 1) is then
1.53·10 -2 Å.
0.
61⋅
λ
δ =
n ⋅sin
β
The practical resolution is much worse than the theoretical diffraction limit. The
main reasons are lens aberrations and in particular the spherical aberration of the
magnetic lenses (see Fig. 3.3) [32]. The spherical aberration causes a stronger bend of
off-axis electrons toward the optical axis, and thus a spot is reproduced as a disk in the
image plane. The radius of this disk is given by Csβ 3 . β is again the semiangle of
collection and Cs the spherical aberration coefficient, which is an important
characteristic of a TEM. With this value and the Rayleigh criterion one can estimated
a practical point-to-point resolution (eqn. 3.2) [32] of the microscope.
r
min
≈ s
( ) 4
1
3
C
0. 91 λ
(3.1)
(3.2)