When electrons pass a specimen they are scattered and a distinction should be
made at this point between two cases:
Elastic scattering, where the energy of the electrons is not altered.
Inelastic scattering, where the electrons lose energy.
Electron optical systems are connected to a significant chromatic aberration and
provide a sharp image only at exactly one energy of the electrons; therefore, inelastic
scattered electrons blur the image. A major part of these electrons are scattered over
a wider angle and therefore they are caught by diaphragms within the system.
Problems with chromatic aberration begin already at the illumination of the system
with electrons. A modern field emission gun for electrons has an inherent energy
spread of typically 0.7 eV, but to obtain maximum resolution even this is too much.
By applying an electron monochromator this energy spread can be reduced to values
less than 0.2 eV.
The second severe source of image blurring in electron microscopy is that of
spherical aberration. This is caused by the fact that the focal length of rays close to the
axis of the microscope is different when compared to that of rays further away from
the optical axis. This leads to imperfect, delocalized pictures and, therefore, limits
the resolution of the system. This occurs because the electrons coming from one
point of an object are not imaged into a single point, but rather into a small disk, thus
blurring the image. The way to avoid rays with a larger distance from the optical axis
is to reduce the numerical aperture. While both chromatic and spherical aberration
will limit the resolution of electron microscopes, conventionally the best electron
microscopes can separate points within a distance of 0.15–0.2 nm.
Since 1936 (in landmark work by Otto Scherzer), it has been acknowledged via a
theoretical, well-based theorem that spherical aberration in electron optics with
rotationally symmetric electron lenses is not correctable. However, in a groundbreaking report, Rose [6] showed that, by combing the electron optical lenses with
multipole electron optical elements, spherical aberration could be reduced by several
orders of magnitude. This paved the road to “sub-A
ngstr€ om” resolution electron
microscopy (A
ngstr€ om is a non-SI length unit; 1 A
¼ 0.1 nm).
The set-up of a modern electron microscope is shown in Figure 12.15. The
electrons are emitted from a field emission point source and accelerated to the
demanded energy, in most cases in the range between 200 and 300 keV. The next
element, the monochromator, selects electrons of a very narrow energy band to
reduce chromatic errors in the optical system. The condenser system (K€ ohler
illumination system) focuses the electrons at the specimen. For high-resolution
scanning electron microscopy a corrector for the spherical aberration (C s corrector)
is necessary in the illumination system. Although in Figure 12.15 the lenses are
shown as light optical lenses, in reality electron microscopes apply magnetic lenses
or, more generally, magnetic electron optical elements.
The picture of the specimen, which is formed by the elastic and inelastic scattering
of electrons within it, is enlarged with the objective lens, after which the electron
beam is limited by the objective lens diaphragm. By correctly selecting the size and
position of this diaphragm it is possible to adjust the contrast and resolution within
352j 12 Characterization of Nanomaterials
made at this point between two cases:
Elastic scattering, where the energy of the electrons is not altered.
Inelastic scattering, where the electrons lose energy.
Electron optical systems are connected to a significant chromatic aberration and
provide a sharp image only at exactly one energy of the electrons; therefore, inelastic
scattered electrons blur the image. A major part of these electrons are scattered over
a wider angle and therefore they are caught by diaphragms within the system.
Problems with chromatic aberration begin already at the illumination of the system
with electrons. A modern field emission gun for electrons has an inherent energy
spread of typically 0.7 eV, but to obtain maximum resolution even this is too much.
By applying an electron monochromator this energy spread can be reduced to values
less than 0.2 eV.
The second severe source of image blurring in electron microscopy is that of
spherical aberration. This is caused by the fact that the focal length of rays close to the
axis of the microscope is different when compared to that of rays further away from
the optical axis. This leads to imperfect, delocalized pictures and, therefore, limits
the resolution of the system. This occurs because the electrons coming from one
point of an object are not imaged into a single point, but rather into a small disk, thus
blurring the image. The way to avoid rays with a larger distance from the optical axis
is to reduce the numerical aperture. While both chromatic and spherical aberration
will limit the resolution of electron microscopes, conventionally the best electron
microscopes can separate points within a distance of 0.15–0.2 nm.
Since 1936 (in landmark work by Otto Scherzer), it has been acknowledged via a
theoretical, well-based theorem that spherical aberration in electron optics with
rotationally symmetric electron lenses is not correctable. However, in a groundbreaking report, Rose [6] showed that, by combing the electron optical lenses with
multipole electron optical elements, spherical aberration could be reduced by several
orders of magnitude. This paved the road to “sub-A
ngstr€ om” resolution electron
microscopy (A
ngstr€ om is a non-SI length unit; 1 A
¼ 0.1 nm).
The set-up of a modern electron microscope is shown in Figure 12.15. The
electrons are emitted from a field emission point source and accelerated to the
demanded energy, in most cases in the range between 200 and 300 keV. The next
element, the monochromator, selects electrons of a very narrow energy band to
reduce chromatic errors in the optical system. The condenser system (K€ ohler
illumination system) focuses the electrons at the specimen. For high-resolution
scanning electron microscopy a corrector for the spherical aberration (C s corrector)
is necessary in the illumination system. Although in Figure 12.15 the lenses are
shown as light optical lenses, in reality electron microscopes apply magnetic lenses
or, more generally, magnetic electron optical elements.
The picture of the specimen, which is formed by the elastic and inelastic scattering
of electrons within it, is enlarged with the objective lens, after which the electron
beam is limited by the objective lens diaphragm. By correctly selecting the size and
position of this diaphragm it is possible to adjust the contrast and resolution within
352j 12 Characterization of Nanomaterials