Katsushige Tsuno

Numerical analysis of trajectories and aberrations of a Wien filter including the effect of fringing fields

Abstract Trajectory equations of a stigmatic Wien filter including the effects of unmatched fringing fields are formulated, and an optimum shape with minimum geometrical aberrations is described. A low-aberration Wien filter is realized under the following conditions: (1) electric and magnetic fields satisfy the orthogonal relation even in the off-axial region, and (2) gap lengths between electrodes and magnetic poles are the same for achieving the balancing condition of electric and magnetic forces in fringing regions. The former condition can be realized by both fields with finite but the same hexapole components; this fact enables us to design a filter with simplified geometry that fulfills the latter condition simultaneously. It is shown that a large deflection of trajectories and resultant aberrations appear if the gap lengths are set to be different.

Third-order aberration theory of Wien filters for monochromators and aberration correctors

Third‐order aberrations at the first and the second focus planes of double focus Wien filters are derived in terms of the following electric and magnetic field components – dipole: E1, B1; quadrupole: E2, B2; hexapole: E3, B3 and octupole: E4, B4. The aberration coefficients are expressed under the second‐order geometrical aberration free conditions of E2 = −(m + 2)E1/8R, B2 = −mB1/8R and E3R2/E1 − B3R2/B1 = m/16, where m is an arbitrary value common to all equations. Aberration figures under the conditions of zero x‐ and y‐axes values show very small probe size and similar patterns to those obtained using a previous numerical simulation [G. Martínez & K. Tsuno (2004) Ultramicroscopy, 100, 105–114]. Round beam conditions are obtained when B3 = 5m2B1/144R2 and (E4/E1 − B4/B1)R3 = −29m2/1152. In this special case, aberration figures contain only chromatic and aperture aberrations at the second focus. The chromatic aberrations become zero when m = 2 and aperture aberrations become zero when m = 1.101 and 10.899 at the second focus. Negative chromatic aberrations are obtained when m < 2 and negative aperture aberrations for m < 1.101. The Wien filter functions not only as a monochromator but also as a corrector of both chromatic and aperture aberrations. There are two advantages in using a Wien filter aberration corrector. First, there is the simplicity that derives from it being a single component aberration correction system. Secondly, the aberration in the off‐axis region varies very little from the on‐axis figures. These characteristics make the corrector very easy to operate.

Third order aberration theory of double Wien filters

The second and the third order aberration theory for a double Wien filter have been analytically developed. A new second order aberration-free condition is found at the image plane of the second filter. This condition is met when b2=−1/4, e2=−1/2, and b3−e3=−1/8, where b2=B2R/B1, e2=E2R/E1, b3=B3R2/B1, and e3=E3R2/E1. Here, R is the cyclotron radius and E1, B1, E2, B2, E3, and B3 are the dipole, quadrupole, and hexapole components of electric and magnetic fields, respectively. This condition is different from the second order aberration-free condition for a single Wien filter, which is satisfied when b2=−3/4, e2=−1, and b3−e3=−3/8. The geometrical second order aberration-free condition has also been found, and requires that e3−b3=(m−1)/8, e2=−m/4, and b2=(1−m)/4. This last set is sufficient to satisfy the above two sets of conditions as well. Residual third order aberrations are calculated for various m. The third order aberrations at the second focus are very small when the new aberration-free condition ...

Magnetic-Field-Free Objective Lens around a Specimen for Observing Fine Structure of Ferromagnetic Materials in a Transmission Electron Microscope

In order to observe the fine structures of ferromagnetic materials or to observe their magnetic domain structures, special magnetic-field-free lenses in which specimens are set in the upper pole-piece have been developed. In these objective lenses, the spherical aberration depends largely on the shape of the lens, especially, (1) the distance between the positions of the specimen and the peak of the lens field, (2) the diameters of the pole-piece bores and the top face of the upper pole-piece, and (3) the gap length. In a lens with a pole-piece of optimum dimensions, the resulting resolution reached 0.7 nm and the leakage field strength was 0.35 mT. Complicated domain structures of ferromagnetic materials could be clearly observed.

Performance of a Monochromator for a 200 kV Analytical Electron Microscope

We have been developing a 200 kV analytical electron microscope, which is equipped with a monochromator [1]. The target performance of the microscope is to achieve an energy resolution of 0.2 eV with a smaller than 2 nm diameter probe on a specimen plane. Though the ultimate energy resolution of 0.14 eV was obtained with our first monochromator, the shape of the beam on the specimen plane was oval [2]. The new monochromator consists of two dodecapole-type Wien-filters (Fig. 1) of 30 mm length and a slit on the symmetric plane of the two filters [2], [3]. The upper (1st) filter and the electro-static round lens at the entrance of the monochromator make an energy-dispersed focus on the slit. The lower (2nd) filter cancels the energy dispersion and makes an achromatic and stigmatic focus at the exit of the monochromator. We obtained the energy dispersion of 19.5 μm/eV on the slit experimentally, which is sufficient to obtain the energy resolution of 0.2 eV using the slit. Figure 2 shows the shape of a 200 keV electron beam on the specimen plane with the new monochromator. It shows that an almost round shaped beam or a better achromatic beam of a 4 nm (FWHM) was obtained. A smaller beam than a 2 nm diameter on the specimen plane at the achromatic condition of the monochromator will be obtained by using a higher excitation condition of the probe forming lens system. We have succeeded in obtaining an energy-dispersed beam on the slit and a stigmatic and achromatic beam at the exit of the monochromator.

Design of omega mode imaging energy filters

Abstract Optical properties of two types of omega filter, A-type and B-type, are compared. The A-type has three focuses in the magnetic field direction ( y ), while the B-type has two. The latter gives a smaller total tilting angle at the entrance and the exit edges and a shorter drift length between the deflection magnets. The effect of the length L L between the window and the pupil planes on the non-isochromaticity is examined under two conditions of a fixed post-filter lens magnification M PL =100 and the optimum magnification M PL (opt). Longer L L is better for isochromatic imaging under the fixed magnification condition M PL =100 times. However, the selection of L L is not so important when the optimum M PL (opt) is used. Three-dimensional field distribution and ray trajectory calculations are made to show the effects of misalignment of the optical axis and mistake of the tilting angle at the entrance and exit edges of the deflection magnets.

Optical properties of immersion objective lenses and collimation of secondary electrons in low-voltage SEM

Optical properties of two kinds of immersion lenses, i.e. the radial gap magnetic lens and the combined electric and magnetic field lens have been compared. When the specimen allows the application of a leakage electric field about 600 V and the accelerating voltage on the specimen is lower than 2 kV, the combined field lens is better than the radial gap lens, because the spherical and chromatic aberration coefficients are small and the collimation efficiency of secondary electrons is perfect. However, if the leakage electric field is not allowed, the radial gap lens is superior to the combined field lens. In the case of the radial gap lens, a weak electric field has to be applied to the specimen for collimating electrons emitted with large angle from the specimen. When the specimen is set lower than the magnetic field maximum position, a solenoid coil placed inside the yoke of the lens is useful to bring up the off axial electrons.

Immersion lenses for low-voltage SEM and LEEM

Spherical and chromatic aberration coefficients Cs and Cc of various immersion lenses for low voltage SEM and LEEM are calculated. The minimum values of magnetic immersion lens are Cs equals Cc equals 1 mm. For the combined electrostatic and magnetic lenses, those values are at most Cs equals 1 mm and Cc equals 0.7 mm, when the specimen is free from the electrostatic field. When the specimen is immersed in the electrostatic field, those values reduce to Cs equals 0.2 mm and Cc equals 0.1 mm at 1 kV.

Modified TEM-STEM for magnetic imaging

Abstract An electron microscope for magnetic imaging (magnetic domain observation) is described. The microscope includes a magnetic-field-free objective lens and a large bulk specimen stage 30 × 50 mm 2 in size. Its resolution as an ordinary transmission electron microscope is 0.7 nm and it has three Lorentz microscopy modes for magnetic imaging: Lorentz TEM (transmission electron microscopy), DPC (differential phase contrast)-STEM (scanning transmission electron microscopy) and Type-2 magnetic contrast SEM (scanning electron microscopy). Resolution of the domain image is 20 nm in the DPC-STEM mode. The minimum magnification for Type-2 SEM is ×5 on a 15×20 mm 2 specimen area. Quantitative measurement of magnetization can be made in DOC and Type-2 imaging because the magnetic contrast is proportional to the magnetic induction.

Inhomogeneity of Magnetic Field of Electromagnet Produced by Parallel Shift of the Central Axis of a Pole Relative to Another Pole

Magnetic field inhomogeneity produced by a parallel shift of the central axis of one pole relative to another was measured. Inhomogeneities proportional to zx and x are induced, where, x is the direction parallel to the shift of the pole axis and z the central axis of the poles. These inhomogeneities proportionally increased with the amount of the shift of the pole axis. Inhomogeneity of the order of 10-6 is induced when the pole axis is shifted by 10-4 times the pole diameter.