178
An Introduction to Beam Physics
of Fig. 7.10 illustrates the effect of the spherical aberration.
The second kind of aberrations are the chromatic aberrations, which
arise as a combination of the opening angle and the energy spread of the
beam. The lowest order chromatic aberration for a round lens is 2, and in
the electrostatic case has the form (x, aδ), which because of symmetry also
equals (y, bδ). These chromatic aberrations are usually denoted by C C . In the
magnetic case after transformation into the appropriate rotated coordinate
system, the situation is again the same. The effect of the chromatic aberration
is illustrated in the bottom picture of Fig. 7.10.
Even in the early days of electron microscopes, the possibility of correcting
the remaining aberrations had been contemplated. Yet the initial result of
theoretical investigation was not very encouraging. Scherzer [62] showed that,
for a round lens without reflection, the spherical and the chromatic aberrations
do not change sign, the same as the focusing force of such a lens (see Section
4.4.1).
Specifically, electrons with a larger angle are focused stronger and electrons
with higher energy are focused weaker. As a result, aberration correction
requires violation of the above assumptions, through using either multipole
elements, electron mirrors or time varying fields. Early attempts on aberration correction, between the late 1940s and the early 1990s, failed mainly due
to insurmountable technical difficulties. Hence the development of electron
microscopes up to the early 1990s follows mainly the line of aberration reduction through optimization of the lens design and improvement of stability.
The initial success of aberration correction came when the technology was
ready in the mid-1990s [59, 39].
7.4.1 Aberration Correction in SEM, STEM and TEM
The first successful aberration correction was reported in 1995, where the
spherical aberration C S and chromatic aberration C C were corrected in a low
voltage SEM (scanning electron microscope). The corrector consists of four
multipole elements (see Fig. 7.11), which was originally proposed in the early
1960s. The two outer elements are electrostatic multipoles and the two inner
ones are superimposed electrostatic and magnetic multipoles. The corrector
consists of two identical quadrupole doublets, where the two quadrupoles
are physically the same, excited at the same current but with opposite polarity.
Furthermore, it is arranged such that the so-called cosine-like ray of the
horizontal plane, which in conventional transfer map terminology corresponds
to the (x, x) matrix element, goes through the center of the left inner element,
while that of the vertical plane goes through the center of the right inner
element. This entails that (x|aδ) and (y|bδ) can be corrected independently
from each other.
More importantly, rays in the vertical plane coincide with those in the
horizontal plane going backwards. This layout minimizes the breaking of rotational symmetry due to the introduction of multipoles. The most noticeable
An Introduction to Beam Physics
of Fig. 7.10 illustrates the effect of the spherical aberration.
The second kind of aberrations are the chromatic aberrations, which
arise as a combination of the opening angle and the energy spread of the
beam. The lowest order chromatic aberration for a round lens is 2, and in
the electrostatic case has the form (x, aδ), which because of symmetry also
equals (y, bδ). These chromatic aberrations are usually denoted by C C . In the
magnetic case after transformation into the appropriate rotated coordinate
system, the situation is again the same. The effect of the chromatic aberration
is illustrated in the bottom picture of Fig. 7.10.
Even in the early days of electron microscopes, the possibility of correcting
the remaining aberrations had been contemplated. Yet the initial result of
theoretical investigation was not very encouraging. Scherzer [62] showed that,
for a round lens without reflection, the spherical and the chromatic aberrations
do not change sign, the same as the focusing force of such a lens (see Section
4.4.1).
Specifically, electrons with a larger angle are focused stronger and electrons
with higher energy are focused weaker. As a result, aberration correction
requires violation of the above assumptions, through using either multipole
elements, electron mirrors or time varying fields. Early attempts on aberration correction, between the late 1940s and the early 1990s, failed mainly due
to insurmountable technical difficulties. Hence the development of electron
microscopes up to the early 1990s follows mainly the line of aberration reduction through optimization of the lens design and improvement of stability.
The initial success of aberration correction came when the technology was
ready in the mid-1990s [59, 39].
7.4.1 Aberration Correction in SEM, STEM and TEM
The first successful aberration correction was reported in 1995, where the
spherical aberration C S and chromatic aberration C C were corrected in a low
voltage SEM (scanning electron microscope). The corrector consists of four
multipole elements (see Fig. 7.11), which was originally proposed in the early
1960s. The two outer elements are electrostatic multipoles and the two inner
ones are superimposed electrostatic and magnetic multipoles. The corrector
consists of two identical quadrupole doublets, where the two quadrupoles
are physically the same, excited at the same current but with opposite polarity.
Furthermore, it is arranged such that the so-called cosine-like ray of the
horizontal plane, which in conventional transfer map terminology corresponds
to the (x, x) matrix element, goes through the center of the left inner element,
while that of the vertical plane goes through the center of the right inner
element. This entails that (x|aδ) and (y|bδ) can be corrected independently
from each other.
More importantly, rays in the vertical plane coincide with those in the
horizontal plane going backwards. This layout minimizes the breaking of rotational symmetry due to the introduction of multipoles. The most noticeable