TY - JOUR
AU - Yasukazu, Murakami,
AB - Abstract The coherency of a 1.2-MV transmission electron microscope was evaluated through illumination semiangles calculated from lengths over which Fresnel fringes can be observed. These lengths were determined from the diameters of circular holes fully filled with Fresnel fringes, i.e. this method allows lengths to be accurately measured even if micrographs are subjected to distortions. The smallest illumination semiangle of 4.0 × 10−9 rad was obtained for a circular hole with a diameter of 191 μm. In addition, electron beam brightness was estimated to be approximately 3 × 1014 A/m2·sr from the obtained illumination semiangle values and current densities. The results provide us with essential information that can be referred to in future electron holography studies aimed at detecting weak electromagnetic fields in materials. coherency, Fresnel fringe, illumination semiangle, brightness The coherency of incident electron beams is an important factor in transmission electron microscopy studies. For example, in Lorentz microscopy, coherency affects the sensitivity in measuring phase shifts due to electromagnetic fields that may exist both inside and outside of specimens. In electron holography, achieving high coherency is particularly important because it improves both interference fringe contrasts and the total number of fringes in electron holograms [1,2]. High coherency can be achieved by making an illumination semiangle β small. A β can be reduced by increasing the brightness of an electron gun, i.e. β is inversely proportional to the square root of brightness B. To improve coherency, field emission (FE) electron guns having high brightness were installed in transmission electron microscopes (TEMs) [3]. Regarding the advancement of electron holography, some of the present authors reported on the development of a 1.2-MV atomic resolution holography TEM [4] (1.2-MV TEM in what follows) equipped with a cold FE electron gun with a superimposed magnetic field [5]. The 1.2-MV TEM has an additional specimen position (referred to as a Lorentz specimen position) that is free from magnetic fields and an objective lens with a spherical aberration corrector [6]. When we realize a small β and atomic order spatial resolution at the Lorentz specimen position, we can observe weak magnetic fields in advanced materials by electron holography with the 1.2-MV TEM. The aim of this study is to determine the illumination semiangle β of the 1.2-MV TEM by examining Fresnel fringes observed in circular holes in metallic plates. Figure 1 shows the optical parameters in a TEM that can be used to determine the illumination semiangle of an electron beam, 2rv, the diameter of a virtual source, a, the distance between the source and a condenser lens, b, the distance between the lens and a beam spot, D, the distance between the lens and specimen plane, d, the distance between the beam spot and specimen plane, and 2rs, the diameter of the beam spot. Since rs=(b/a)rv, β is given by β=rsd=rva(Dd−1). (1) Fig. 1. View largeDownload slide Schematic of illumination optics. Illumination angle 2β was determined with beam spot diameter 2rs and distance d between beam spot and specimen plane. Fig. 1. View largeDownload slide Schematic of illumination optics. Illumination angle 2β was determined with beam spot diameter 2rs and distance d between beam spot and specimen plane. We note that β≤(a/D)αv, where αv is the convergence angle of the virtual source determined by a condenser aperture, indicating that the maximum value for β does not exceed αv on the specimen plane [7]. From Eq. (1), a smaller illumination semiangle can be achieved by increasing d and/or decreasing the radius rs using the condenser lens. Moreover, to make the rs and rv small, we need to reduce noises that give trajectory displacements and angular deflections in the electron movement (deflection noises in what follows). For that purpose, we analyzed Lissajous figures with deflection noises using an optical system shown in Fig. 2 [8]. Sinusoidal coil currents with a 90-degree phase difference were supplied from the oscillators A and B to alignment (AL) X and Y coils located under the magnification lens. When electron beams include deflection noise, Lissajous figures on the screen show their directions, amplitudes, and frequencies. Fig. 2. View largeDownload slide Schematic of optical system for obtaining Lissajous figures. Two oscillators A and B supply sinusoidal coil currents with phase different of 90 degrees for AL X and Y coils. Wave forms of the deflection noise are displayed as Lissajous figures on the screen. Directions, amplitudes, and frequencies of the noise are determined by analyzing their differences from the circular Lissajous figures. Fig. 2. View largeDownload slide Schematic of optical system for obtaining Lissajous figures. Two oscillators A and B supply sinusoidal coil currents with phase different of 90 degrees for AL X and Y coils. Wave forms of the deflection noise are displayed as Lissajous figures on the screen. Directions, amplitudes, and frequencies of the noise are determined by analyzing their differences from the circular Lissajous figures. The Lissagous figure analysis was applied to the optics in the 1.2-MV TEM, which resulted in visualizing deflection noises having frequencies of about 1 and 70 kHz. To decrease these noises, bipolar capacitors and zipper type shield tubes were placed at the current power supply and around cables, respectively. In this way, the deflection noises were decreased down to 30% of the original value. Next we discuss Fresnel fringes, which are observed near the edges of a specimen. When an edge of a specimen is illuminated by a nearly plane-electron wave, Fresnel fringes are formed on a defocus plane placed at a distance Mε from the image plane, where M is the magnification of an objective lens and ε is a defocus value from the specimen plane. The length L over which the Fresnel fringes can be observed is given by L=λ/2β, where λ is the wavelength of the incident electron and L is equal to a coherence length [3]. Then by measuring L, we can determine the illumination semiangle β(=λ/2L). The length L was evaluated with a large defocus value and a low magnification, although these conditions may cause significant image distortions [9]. To determine L accurately from a micrograph subjected to distortions, we measured the diameters of circular holes in metallic plates [10,11] that were fully filled with Fresnel fringes. When the fringes are observed at the center of the holes, L is equal to or greater than rc. Then, illumination semiangles β are estimated from the relationship β=λ/2L≤λ/2rc. To deduce the β from observations of L, circular holes having diameters of 20.9, 32.9, 62.9, 83.8, 104.0, 124.5, and 154.5 μm were fabricated by using a focused ion beam apparatus (NB5000, Hitachi High-Technologies Corp.) on thin copper foil (thickness 30 μm). In addition, another circular hole with a diameter of 191.0 μm, which was the largest in our experiments, was made by an osmium-coated molybdenum plate. The experimental conditions were as follows: the accelerating voltage was 1.2 MV, the total emission current of the electron beam was about 15 μA, and the circular holes were placed at the specimen position. Micrographs were acquired under an under-focus condition. Fresnel fringes were recorded on a direct detection CMOS camera (K2 Summit Camera, Gatan, Inc.) with a pixel size of 5 × 5 μm and exposure times of 1–10 seconds. Figure 3a shows a picture of circular hole with a 20.9-μm diameter fully filled with Fresnel fringes. The exposure time was 1 second. The estimated value of β was smaller than 3.6 × 10−8 rad. Figure 3b shows a picture of 191.0-μm diameter hole fully filled with Fresnel fringes. The exposure time was 5 seconds. Because of significant image distortion, we did not provide a scale bar. The center part of the circular hole was brighter than the surrounding area, probably due to influence of lens aberrations because the optical condition was adjusted to obtain a defocus value of several dozen meters. Figure 3c shows an intensity profile measured along a line crossing the center of the circular hole (measured from the left edge to the right edge in Fig. 3b). Figure 3d provides an enlarged intensity profile for the region indicated by a rectangle in Fig. 3c. Figure 3d indicates that the circular hole was fully filled with Fresnel fringes, and, therefore, L was estimated to be larger than 95.5 μm, indicating β ≤ 4.0 × 10−9 rad. Fig. 3. View largeDownload slide (a) Circular hole with diameter of 20.9 μm fully filled with Fresnel fringes. Distance d between beam spot and specimen position plane was 149 mm. (b) Circular hole with diameter of 191.0 μm fully filled with Fresnel fringes. Distance d was adjusted to 384 mm to observe Fresnel fringes clearly. (c) Intensity profile crossing center of circular hole from left edge to right edge of Fig. 3b. (d) Enlarged intensity profile at center of Fig. 3c. Fresnel fringes were observed at the center of circular hole with diameter of 191.0 μm. Fig. 3. View largeDownload slide (a) Circular hole with diameter of 20.9 μm fully filled with Fresnel fringes. Distance d between beam spot and specimen position plane was 149 mm. (b) Circular hole with diameter of 191.0 μm fully filled with Fresnel fringes. Distance d was adjusted to 384 mm to observe Fresnel fringes clearly. (c) Intensity profile crossing center of circular hole from left edge to right edge of Fig. 3b. (d) Enlarged intensity profile at center of Fig. 3c. Fresnel fringes were observed at the center of circular hole with diameter of 191.0 μm. Figure 4 plots obtained β as a function of d estimated from the condenser lens current, where vertical error bars indicate measurement errors of circular hole-diameters using a scanning electron microscope. The shaded area above the curve indicates where circular holes are fully filled with Fresnel fringes. The smallest value of β of 4.0 × 10−9 rad was obtained at d≥364mm. The solid line indicates a theoretical curve that shows the relationship between β and d given by Eq. (1). The observed data shown in solid circles can be reasonably explained by Eq. (1) with the three values: rv = 40 nm, a = 2.0 m, and D = 416 mm. These values were simulated using the electron optic simulation program (Wien-Refine 5, Munro’s Electron Beam Software Ltd., London). Fig. 4. View largeDownload slide Illumination semiangles β as a function of distance d from beam spot position to specimen position. The shaded area above the curve indicates where circular holes are fully filled Fresnel fringes. β was obtained to be 4.0 × 10−9 rad at d ≥ 364 mm. Fig. 4. View largeDownload slide Illumination semiangles β as a function of distance d from beam spot position to specimen position. The shaded area above the curve indicates where circular holes are fully filled Fresnel fringes. β was obtained to be 4.0 × 10−9 rad at d ≥ 364 mm. The minimum β calculated using Eq. (1) was about 1 × 10−9 rad at dmax = 396 mm, which can be obtainable by further decreasing deflection noises in electron beams. We note that detecting smaller β requires a longer exposure time because of darker electron micrographs. For that, further improvement of mechanical stability is necessary. The smallest value for β of 4.0 × 10−9 rad, achieved by using the 1.2-MV TEM, appears to be highly advantageous for phase shift measurements. In fact, this value is two orders of magnitude smaller than that of the magnetic deflection angle observed in vortices in high-Tc superconductors [12] or skyrmions in Fe0.5Co0.5Si thin films [13]. Once β is determined, the electron beam brightness B can be estimated from B=i/πβ2 [14], where i is the current density of the electron beam at the specimen plane. First, we discuss current densities measured by using a Faraday cup. Under the present experimental conditions, the area of the Faraday cup was 1/100 to 1/200 smaller than that of the illumination area. The total emission currents of the electron beam were 13–15 μA. The measured i were i = 123 μA/cm2 at β = 3.6 × 10−8 rad, i = 50.9 μA/cm2 at β = 2.3 × 10−8 rad, and i = 16.2 μA/cm2 at β = 1.2 × 10−8 rad. From these data, we determined the electron beam brightness B to be approximately equal to 3.0–3.6 × 1014 A/m2·sr. Using the obtained brightness B, the maximum number of electron biprism interference fringes nmax achieved by using an electron biprism can be calculated from the relationship nmax=λ/4sIexpBπt [3]. Here s is film resolution, Iexp is electron dose to film, and t is exposure time. The calculated nmax is expected to be more than 15 000, which is about 1.3 times larger than that of the value attained by using the previously developed 1.0-MV TEM [15]. Here, we used s = 5 μm, Iexp = 1 × 10−10 C/cm2, and t=180s [16]. In conclusion, we obtained an illumination semiangle of 4.0 × 10−9 rad through the comprehensive analysis of Fresnel fringes with a 1.2-MV TEM. Then, the electron beam brightness was estimated to be about 3 × 1014 A/m2·sr from illumination semiangles and current densities at the specimen position. The high coherency performance of this microscope makes it possible to observe electromagnetic fields at high resolution and sensitivity. Acknowledgments The authors are grateful to T. Kawasaki of Hitachi, Ltd. and K. Shimada of RIKEN for their valuable discussions and technical support. Funding The development of 1.2-MV TEM was supported by a grant from the Japan Society for the Promotion of Science through the ‘FIRST Program’ initiated by the Council for Science, Technology, and Innovation. References 1 Lichte H ( 2008 ) Performance limits of electron holography . Ultramicroscopy 108 : 256 – 262 . Google Scholar Crossref Search ADS PubMed 2 Tonomura A ( 1999 ) Electron holography , 2nd edn , pp 15 – 19 ( Springer Verlag , Berlin ). 3 Tonomura A , Matsuda T , Endo J , Todokoro H , and Komoda T ( 1979 ) Development of a field emission electron microscope . J. Electron Microsc. 28 ( 1 ): 1 – 11 . 4 Akashi T , Takahashi Y , Tanigaki T , Shimakura T , Kawasaki T , Furutsu T , Shinada H , Müller H , Haider M , Osakabe N , and Tonomura A ( 2015 ) Aberration corrected 1.2-MV cold field emission transmission electron microscope with a sub-50-pm resolution . Appl. Phys. Lett. 106 : 074101 . Google Scholar Crossref Search ADS 5 Kasuya K , Kawasaki T , Moriya N , Arai M , and Furutsu T ( 2014 ) Magnetic field superimposed cold field emission gun under extreme-high vacuum . J. Vac. Sci. Technol. B 32 : 031802 . Google Scholar Crossref Search ADS 6 Takahashi Y , Akashi T , Shimakura T , Tanigaki T , Kawasaki T , Shinada H , and Osakabe N ( 2015 ) Resolution assessment of an aberration corrected 1.2-MV field emission transmission electron microscope . Microsc. Microanal. 21 ( Suppl 3 ): 1865 – 1866 . Google Scholar Crossref Search ADS 7 Hirsch P B ( 1965 ) Electron microscopy of thin crystals , pp 15 – 18 ( Butterworths , London ). 8 Tonomura A ( 1998 ) The quantum world unveiled by electron waves , pp 42 – 43 ( World Scientific , Singapore ). 9 Reimer L ( 1984 ) Transmission electron microscopy , pp 41 – 43 ( Springer Verlag , Berlin ). 10 Houdellier F , Masseboeuf A , Monthioux M , and Hÿtch M J ( 2012 ) New carbon cone nanotip for use in a highly coherent cold field emission electron microscope . Carbon N. Y. 50 ( 5 ): 2037 . Google Scholar Crossref Search ADS 11 Yamasaki J , Shimaoka Y , and Sasaki H ( 2018 ) Precise method for measuring spatial coherence in TEM beams using airy diffraction patterns . Microscopy . doi:10.1093/jmicro/dfx093 . 12 Harada K , Matsuda T , Bonevich J , Igarashi M , Kondo S , Pozzi G , Kawabe U , and Tonomura A ( 1992 ) Real-time observation of vortex lattices in a superconductor by electron microscopy . Nature 360 : 51 – 53 . Google Scholar Crossref Search ADS 13 Park H S , Yu X , Aizawa S , Tanigaki T , Akashi T , Takahashi Y , Matsuda T , Kanazawa N , Onose Y , Shindo D , Tonomura A , and Tokura Y ( 2014 ) Observation of the magnetic flux and three dimensional structure of skyrmion lattices by electron holography . Nat. Nanotechol. 9 : 337 – 342 . Google Scholar Crossref Search ADS 14 Reimer L ( 1984 ) Transmission electron microscopy , pp 89 – 92 ( Springer Verlag , Berlin ). 15 Kawasaki T , Matsui I , Yoshida T , Katsuta T , Hayashi S , Onai T , Furutsu T , Myouchin K , Numata M , Mogaki H , Gorai M , Akashi T , Kamimura O , Matsuda T , Osakabe N , Tonomura A , and Kitazawa K ( 2000 ) Development of 1 MV field emission transmission electron microscope . J. Electron Microsc. 49 ( 6 ): 711 – 718 . Google Scholar Crossref Search ADS 16 Akashi T , Harada K , Matsuda T , Kasai H , Tonomura A , Furutsu T , Moriya N , Yoshida T , Kawasaki T , Kitazawa K , and Koinuma H ( 2002 ) Record number (11 000) of interference fringes obtained by a 1 MV field-emission electron microscope . Appl. Phys. Lett. 81 ( 10 ): 1922 – 1924 . Google Scholar Crossref Search ADS © The Author(s) 2018. Published by Oxford University Press on behalf of The Japanese Society of Microscopy. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model)
TI - Illumination semiangle of 10−9 rad achieved in a 1.2-MV atomic resolution holography transmission electron microscope
JF - Microscopy
DO - 10.1093/jmicro/dfy031
DA - 2018-10-01
UR - https://www.deepdyve.com/lp/oxford-university-press/illumination-semiangle-of-10-9-rad-achieved-in-a-1-2-mv-atomic-Hk53zLWyfT
SP - 286
VL - 67
IS - 5
DP - DeepDyve
ER -