Properties of electrostatic correcting systems with annular apertures

Microscopy ◽  
2019 ◽  
Author(s):  
Tetsuji Kodama ◽  
Tadahiro Kawasaki ◽  
Takashi Ikuta
Keyword(s):  
Circular Hole ◽  
Electrostatic Field ◽  
Deflection Angle ◽  
Optical Axis ◽  
Spherical Aberration ◽  
Focal Length ◽  
Electrostatic Lens ◽  
Annular Aperture ◽  
Analytical Formulae ◽  
Electron Microscopes

Abstract Image formation in electron microscopes with circular hole and annular apertures is studied theoretically. The apertures—the circular hole aperture being negative with respect to the annular aperture—produce an additional electrostatic field that exerts a force on the electrons directed toward the optical axis. The resulting deflection angle decreases with increasing distance from the optical axis. This electrostatic field results in a correcting effect of the unavoidable spherical aberration of round electron lenses; the deflection toward the optical axis increases stronger than linearly with increasing distance from the optical axis. Analytical formulae are given for the correcting effect of circular hole and annular apertures. The expressions are based on the Davisson–Calbick formula, which is used to calculate focal length of a simple electrostatic lens.

Experimental Study on Correction of Spherical Aberration in Electro-Magnetic Round Lens

1990 ◽  
Vol 48 (1) ◽  
pp. 234-235
Author(s):  
Ergang Chen ◽  
Chongjun Mu
Keyword(s):  
Electron Beam ◽  
Spherical Aberration ◽  
Focal Length ◽  
Image Point ◽  
Electron Trajectory ◽  
Optical Instruments ◽  
Concave Lens ◽  
In Series ◽  
Electron Microscopes ◽  
Electro Magnetic

As we know that the spherical aberration in a round electromagnetic lens can not be eliminated. Therefor,the correcting of such aberration is an important subject to improve the ultimate resolution of electron microscopes and the performance of other electron optical instruments, such as electron beam manufactureing machines, electron lithographic machine etc.A combination of quadrupoles and octupoles which was proposed by Scherzer is a reasonable way to correct this aberration, but it has been proved practically unsuccessful. Crewe suggested that the sextu-pole elements could be used as a device to correct the 3rd order aberration of a round lens. Later he has showed that a system of two sextupoles with a round lens placed in the middle of it can acturely act as an electromagnetical concave lens if the focal length of this middle lens be settled to satisfy certain condition. Instead of taking terms of z7 in series solution of motion equation of electron in sextu-pole which Crewe had done, we took it up to z20to compute the amplitude r and slope r' of electron trajectory at each specific point z1 , z2 , z3, and z4along the optical axis. The results show that the action of sex-tupole-lens-sextupole system does act as an optical concave lens. It produces a negative spherical aberration. Differing from optical concave lens, in this system the negative aberration can be varied in a wide rang by adjusting the strength of sextupole k. Fig.2 shows a series of computed performances of electron beam near Gaussian image point while the strength of sextupole k=0 incase(a) and k1< k2in case (b) and (c). Evidently, this system does produce a negative spherical aberration while k is not zero.

Beyond One Angstrom

1990 ◽  
Vol 48 (1) ◽  
pp. 204-205
Author(s):  
Albert. V. Crewe
Keyword(s):  
Electron Microscopy ◽  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Low Energy ◽  
Objective Lens ◽  
Squeeze Out ◽  
Electron Microscopes

I believe everyone would agree we have just about reached the limit of performance of today's electron microscopes. This is not to say that additional advances will not take place, because there is always one more drop of blood to squeeze out. But it is certainly becoming increasingly apparent that we can not expect more out of the magnetic lenses that we now have. I am sure that everyone who has ever been concerned with this problem has arrived at the same set of conclusions but it may help to set them down one more time.The available resolution in electron microscopy is distressingly poor compared to the wavelength of the electrons. The culprit is always the objective lens. For low energy, say less than 5,000 volts, chromatic aberration is the offending element whereas at high voltages it is the spherical aberration coefficient which we must be concerned with. In both cases, there are some basic restrictions which apply. In the case of chromatic aberration it is always very closely equal with the focal length of the lens and for the spherical aberration coefficient the best we can do is about 1/4 or 1/2 the focal length.

Chromatic Aberration Correction of a Low-Voltage SEM using a Wien Filter: Adjusting the Correction Strength

2001 ◽  
Vol 7 (S2) ◽  
pp. 874-875
Author(s):  
T. Steffen ◽  
P.C. Tiemeijer ◽  
M.P.C.M. Krijn ◽  
S.A.M. Mentink
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Objective Lens ◽  
Aberration Correction ◽  
Wien Filter ◽  
Electron Microscopes ◽  
Working Distance ◽  
Scanning Electron Microscopes

The resolution of state-of-the-art low-voltage scanning electron microscopes (LV SEM), which is currently limited by the chromatic and spherical aberrations of the objective lens, can be improved by incorporating an aberration correcting device. At present four different concepts are discussed in literature: Zach and Haider demonstrated that a quadrupole/octupole corrector can correct both chromatic and spherical aberration. Rose proposed a Wien filter for chromatic aberration correction, which has relaxed stability requirements. Recently, we reported a simplified version of this corrector and showed that a spherical aberration corrector can be integrated in a Wien filter. Henstra and co-workers suggested a purely electrostatic corrector that can correct both chromatic and spherical aberration.For all these concepts problems may arise when the lens-to-sample (working) distance for an aligned corrector is to be changed. in general, the corrector settings depend on the ratio Cc/f2, where Cc and f denote the coefficient of the chromatic aberration and the focal length of the objective lens, respectively. When the working distance is changed, this ratio is no longer perfectly matched to the corrector settings. The tedious realignments and readjustments, which then seem necessary, can be avoided by using a doublet objective lens as illustrated schematically in Figure 1.

Resolution Attainable With the Present Day STEM

1973 ◽  
Vol 31 ◽  
pp. 230-231 ◽  
Author(s):  
J. S. Wall ◽  
J. P. Langmore ◽  
H. Isaacson ◽  
A. V. Crewe
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Aperture Size ◽  
Magnetic Lens ◽  
Peak Intensity ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Half Angle

The scanning transmission electron microscope (STEM) constructed by the authors employs a field emission gun and a 1.15 mm focal length magnetic lens to produce a probe on the specimen. The aperture size is chosen to allow one wavelength of spherical aberration at the edge of the objective aperture. Under these conditions the profile of the focused spot is expected to be similar to an Airy intensity distribution with the first zero at the same point but with a peak intensity 80 per cent of that which would be obtained If the lens had no aberration. This condition is attained when the half angle that the incident beam subtends at the specimen, 𝛂 = (4𝛌/Cs)¼

The Reduction of Chromatic Aberrations Due to Instrumental Instabilities

1971 ◽  
Vol 29 ◽  
pp. 14-15
Author(s):  
J. S. Lally ◽  
R. Evans
Keyword(s):  
Electron Microscope ◽  
High Voltage ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Objective Lens ◽  
Usual Practice ◽  
Voltage Electron ◽  
Short Focal Length ◽  
Chromatic Aberrations ◽  
Electron Microscopes

One of the instrumental factors often limiting the resolution of the electron microscope is image defocussing due to changes in accelerating voltage or objective lens current. This factor is particularly important in high voltage electron microscopes both because of the higher voltages and lens currents required but also because of the inherently longer focal lengths, i.e. 6 mm in contrast to 1.5-2.2 mm for modern short focal length objectives.The usual practice in commercial electron microscopes is to design separately stabilized accelerating voltage and lens supplies. In this case chromatic aberration in the image is caused by the random and independent fluctuations of both the high voltage and objective lens current.

Improvements in the electron probe forming capabilities and x-ray hole counts in the Philips TEM

1983 ◽  
Vol 41 ◽  
pp. 376-377
Author(s):  
Richard L. McConville
Keyword(s):  
Field Strength ◽  
Electron Probe ◽  
Spherical Aberration ◽  
Focal Length ◽  
Objective Lens ◽  
Parallel Beam ◽  
Tilt Axis ◽  
X Ray ◽  
Small Probe ◽  
Specimen Height

A second generation twin lens has been developed. This symmetrical lens with a wider bore, yet superior values of chromatic and spherical aberration for a given focal length, retains both eucentric ± 60° tilt movement and 20°x ray detector take-off angle at 90° to the tilt axis. Adjust able tilt axis height, as well as specimen height, now ensures almost invariant objective lens strengths for both TEM (parallel beam conditions) and STEM or nano probe (focused small probe) modes.These modes are selected through use of an auxiliary lens situ ated above the objective. When this lens is on the specimen is illuminated with a parallel beam of electrons, and when it is off the specimen is illuminated with a focused probe of dimensions governed by the excitation of the condenser 1 lens. Thus TEM/STEM operation is controlled by a lens which is independent of the objective lens field strength.

Comparison of Deterministic and Linear Cosine Spatial Filtering of Transmission Electron Micrographs

1972 ◽  
Vol 30 ◽  
pp. 596-597
Author(s):  
David A. Ansley
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Spatial Filter ◽  
Operating Conditions ◽  
Objective Lens ◽  
List Type ◽  
Spatial Filters ◽  
Transmission Electron ◽  
Wide Range

The coherence of the electron flux of a transmission electron microscope (TEM) limits the direct application of deconvolution techniques which have been used successfully on unmanned spacecraft programs. The theory assumes noncoherent illumination. Deconvolution of a TEM micrograph will, therefore, in general produce spurious detail rather than improved resolution.A primary goal of our research is to study the performance of several types of linear spatial filters as a function of specimen contrast, phase, and coherence. We have, therefore, developed a one-dimensional analysis and plotting program to simulate a wide 'range of operating conditions of the TEM, including adjustment of the:(1) Specimen amplitude, phase, and separation(2) Illumination wavelength, half-angle, and tilt(3) Objective lens focal length and aperture width(4) Spherical aberration, defocus, and chromatic aberration focus shift(5) Detector gamma, additive, and multiplicative noise constants(6) Type of spatial filter: linear cosine, linear sine, or deterministic

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

A High Resolution Scanning Microscope

1968 ◽  
Vol 26 ◽  
pp. 356-357
Author(s):  
A. V. Crewe ◽  
J. Wall ◽  
L. M. Welter
Keyword(s):  
High Resolution ◽  
Field Emission ◽  
Spherical Aberration ◽  
Focal Length ◽  
Spot Size ◽  
Emission Source ◽  
Field Of View ◽  
Scanning Microscope ◽  
Magnetic Lens ◽  
High Quality

A scanning microscope using a field emission source has been described elsewhere. This microscope has now been improved by replacing the single magnetic lens with a high quality lens of the type described by Ruska. This lens has a focal length of 1 mm and a spherical aberration coefficient of 0.5 mm. The final spot size, and therefore the microscope resolution, is limited by the aberration of this lens to about 6 Å.The lens has been constructed very carefully, maintaining a tolerance of + 1 μ on all critical surfaces. The gun is prealigned on the lens to form a compact unit. The only mechanical adjustments are those which control the specimen and the tip positions. The microscope can be used in two modes. With the lens off and the gun focused on the specimen, the resolution is 250 Å over an undistorted field of view of 2 mm. With the lens on,the resolution is 20 Å or better over a field of view of 40 microns. The magnification can be accurately varied by attenuating the raster current.

Chromatic aberration and low-voltage SEM

1987 ◽  
Vol 45 ◽  
pp. 546-547
Author(s):  
Zhifeng Shao ◽  
A.V. Crewe
Keyword(s):  
Electron Energy ◽  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Primary Electron ◽  
Probe Size ◽  
Non Local ◽  
Optical Treatment ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

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