A Novel Monochromator with Double Cylindrical Lenses
Takashi Ogawa, Boklae Cho, Sang Jung Ahn
Center for Advanced Instrumentation, Division of Industrial Metrology, Korea Research Institute of
Standards and Science, Daejeon, Republic of Korea
Recently, various types of monochromators (MCs) have been proposed for advanced instruments such
as the (scanning) transmission electron microscope ((S)TEM) [1,2], the scanning electron microscope
(SEM) [3], and microscopes that utilize electron energy loss spectroscopy (EELS). There are several
advantages with regard to the use of MCs. First, these devices offer improvements in the spatial
resolution in low-energy regimes by reducing the contribution of chromatic aberrations. Second, they
offer improvements in the energy resolution of the EELS spectra. Further improvements are necessary to
reveal new information about specimens, such as the phonon signals. In addition, industry applications
require simple and robust structures for MCs. In this study, we propose a novel MC with a high energy
resolution and a simple structure. It consists of two electrostatic cylindrical lenses (CLs) in highly
excited retarding mode, similar to a Möllenstedt energy analyzer [4]. They are placed in mid-plane
symmetry and both are shifted from the optical axis of a microscope. A detailed discussion of the MC is
given below.
For this MC, an offset CL is a key component. We give an outline of its physical behavior. A CL
consists of three electrodes, similar to an Einzel lens but with rectangular openings in the center. This
offers a stronger focusing effect in the X direction of the shorter side of the openings and a weaker focus
in the Y direction. The electrons travel in the Z direction. The electrostatic potential of a CL can be
expressed as follows:
(, , ) ≅ () −
′′
()
2
4 ⁄ +⋯ . (1)
Ohiwa introduced the idea of a moving objective lens (MOL), which shows that superposition of a
deflection field on a lens field is equivalent to displacement of the lens [5]. If the displacement of a CL
is X
d
, the potential of the offset CL is given by
( −
, , ) ≅ (, , ) −
+ ⋯ ≅ () −
′′
()
2
4
+
′′
()
2
+⋯ .
(2)
The third term corresponds to the deflection effect caused by the displacement X
d
. The deflection
function can be expressed as
1
() =
′′
() 2 ⁄ . (3)
Smith and Munro derived a unified aberration theory for electrostatic lenses and multipoles [6]. We
apply their theory to offset CLs. The paraxial ray equation can be written as follows:
′′
+ ′′ 2 ⁄ + ′′ 4 ⁄ =
1
2 ⁄ . (4)
Two independent, homogeneous solutions of Eq. 3 can be written as an axial ray x
a
and a field ray x
b
.
The inhomogeneous form of Eq. 3 can be solved by the variation of parameters method. The solution x
c
can be written as
() =
()
√(
0
)
∫
1
()
()
2√()
−
()
√(
0
)
∫
1
()
()
2√()
. (5)
Eq. 5 shows that defection function F
1x
produces deflection ray x
c
. The energy deviation, ∆ϕ, causes
displacement δx
c
to the original position of the trajectories. Here, δx
c
includes not only the axial and
transverse chromatic aberrations of the CL but also the displacement x
κ
for deflection ray x
c
, which takes
κ
= Δ
(
) (
), ⁄ where =⌊
√
′
⌋
∫
′′
√
.
(6)
112
doi:10.1017/S1431927615013239 © Microscopy Society of America 2015
https://doi.org/10.1017/S1431927615013239 Published online by Cambridge University Press