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Design of a mirror aberration corrector and a beam separator for LEEM
Applied Surface Science 256 (2009) 1035–1041
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Design of a mirror aberration corrector and a beam separator for LEEM K. Tsuno a,b,*, T. Yasue a, T. Koshikawa a a b
Fundamental Electronics Research Institute, Osaka Electro-Communication Univ., Japan Electron Optics Solutions Tsuno, Japan
A R T I C L E I N F O
A B S T R A C T
Article history: Available online 6 June 2009
A SPLEEM (spin polarized low energy electron microscope) has been designed with a numerical simulation of electrostatic and magnetic field distributions and electron ray trajectories. Highly (more than 90%) spin polarized electron source has been used. A Wien type spin manipulator and a magnetic lens type spin rotator are used to align spin direction. A magnetic field free objective lens is designed to observe magnetic domain structure of magnetic materials. High or low magnification mode can be selected by using a combined electrostatic and magnetic objective lens for a high spatial resolution and a wide imaging area observation. An electrostatic mirror aberration corrector is installed after the image forming objective lens. A double deflection 458 beam separator is used to bend the direction of electrons from the source to the objective lens and from the objective lens to the mirror aberration corrector. ß 2009 Elsevier B.V. All rights reserved.
PACS: 41.85.Gy, 41.85.Lc Keywords: LEEM, SPLEEM, Mirror corrector, Beam separator, Cathode lens
1. Introduction Lorentz microscopy is a popular magnetic domain observation method with a transmission electron microscope (TEM/STEM). A drawback of Lorentz microscopy is its necessity of thin film specimen. It is well known that magnetic domain structure depends largely on the specimen shape. Bulk specimens can be observed in SEM and LEEM/PEEM. The origin of Type-I and Type-II magnetic contrast of SEM [1] is the Lorentz force. Type-I magnetic contrast uses leakage fields above the specimen similar to AFM. Type-II magnetic contrast in SEM has been used in practical magnetic materials such as a magnetic head [2] and a Si-steel. The former is used under the working frequencies and the latter is observed through the insulating coating [3]. The key technologies used are the lock-in amplifier in the former case and the high accelerating voltage in the latter case. Spin-SEM (or SEMPA) [4] does not use the Lorentz force. It analyzes the spin polarization ratio of the secondary electrons. PEEM with a circular polarized synchrotron radiation source [5] and spin polarized LEEM (SPLEEM) [6] are also the direct imaging bulk magnetic domain observation method. Among those methods, we shall compare two methods of Spin SEM and SPLEEM. 1. Vacuum: Spin SEM can be used lower vacuum than SPLEEM. 2. Objective lens: Spin SEM usually uses magnetic lens. However, SPLEEM can use totally electrostatic objective lens to avoid leakage magnetic field from the magnetic lens. 3.
* Corresponding author at: Electron Optics Solutions Tsuno 2-10-11, Mihori, Akishima, Tokyo 186-0001, Japan. Tel.: +81 42 544 9803; fax: +81 42 544 9803. E-mail address: [email protected] (K. Tsuno). 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.05.114
Detector: In spin SEM, detection system must be inserted at the gap between the objective lens and the specimen. This makes the working distance (WD) longer than the usual SEM and destroys the spatial resolution. In SPLEEM, nothing is necessary around the specimen. 4. Specimen: Spin SEM can be used in practical magnetic materials and has succeeded in observing 20 nm or less bit length of the recording media [7]. SPLEEM can be used exclusively for the specimens with a LEED pattern. It is hard to use the polycrystalline practical materials. 5. In situ observation: Spin SEM need a time to take a picture and not possible in using it under in situ condition. SPLEEM can be used in real time in principle. However, at present, it has only a low magnetic contrast due to the low spin polarization factor (about 20–30%) [8] and relatively low performance of LEEM prevent in situ observation. Although many advantages of SPLEEM in magnetic domain observation in principle, LEEM itself has various drawbacks compared to the other electron microscopes. Low spatial resolution is a typical example. In low magnification, fairly large area must be illuminated. On the other hand, at high magnifications, illumination area must be concentrated to get a bright image. However, in order to get a focused image in the image forming side, the objective lens must be used under the focused state. The same lens field is used both for the illumination and image forming objective lenses. This means that the objective lens condition is not perfect for the illumination. In the case of TEM, different regions of the objective lens field are used as the illumination and image forming lenses. The illumination field is weaker than that of the image forming field (conventional mode). Even if the condenser-objective condition (the same excitation fields between the illumination and the image forming region) is used, third condenser lens is added just
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Fig. 1. Electron beam illumination system. (A) Spin polarized electron source, (B) LaB6 electron source, (C) spin manipulator, (D) beam selector, (E) condenser lenses and spin rotator, and (F) beam separator and objective lens.
above the objective lens to spread out the illumination beam. However, the same third condenser lens cannot be put after the objective lens in LEEM, because there is a beam separator just after the objective lens. It is difficult to change the illumination area by the condenser lenses. This results either the low brightness at high magnification or a narrow illumination area in the low magnification. Relatively low spatial resolution of LEEM is a result of large aberrations of the objective lens and the large wave length of electrons due to the low accelerating voltage near the specimen. Aberration corrector has been attached to improve the resolution. A mirror corrector [9] has an axially symmetric structure and therefore suitable for the direct imaging microscopes. It needs a beam separator to separate the incident beam and the reflected beam. LEEM already has a beam separator between the illumination and image forming beams. Double beam separator has an advantage of cancelling the dispersion and the second order geometrical aberrations of the beam separator. By this reason, the mirror corrector is suitable for LEEM [10]. The present investigation focuses firstly on to improve the optical performance of LEEM. Optics of LEEM exists behind TEM and SEM. Experiences for designing TEM and SEM are applied to the design of a new LEEM to improve the performance of the condenser and objective lenses. Secondly, the LEEM is combined to the highly spin polarized electron source to make an SPLEEM. Spin manipulator design is also improved. Thirdly, simulation for a mirror aberration corrector has been made.
compensate the spin rotation, to enable higher accelerating voltages of 10–20 kV. Three double gap magnetic lenses are used to condense the illumination beam. The illumination area can be changed both by the second condenser lens (E in Fig. 1) and the objective lens (bottom right of F in Fig. 1). Beam separator (top left of F in Fig. 1) separates the direction of the illumination beam and the image forming beam. The objective lens consists of a cathode lens combined with the electrostatic and magnetic lenses. The
2. Illumination system Fig. 1 shows an illumination system of our SPLEEM. It has two electron guns; (1) a spin polarized electron gun (A in Fig. 1) and (2) a LaB6 gun (B in Fig. 1). The former consists of a strained superlattice thin film cathode based on GaAsP/GaAs semiconductor [11,12] and a pulsed laser beam which illuminates the cathode from the back of the film [11]. The selection of the gun is made by switching on (LaB6 gun) or off (spin gun) the 908 deflection beam selector (D of Fig. 1). Detailed spin polarization properties are described in reference [11]. A gun lens (the latter half of A: in Fig. 1) is used to make a parallel electron beam. There are two spin manipulators to rotate the electron spins into a plane perpendicular to the beam direction (C) and a rotation about the beam direction (E), respectively. The former spin manipulator made by a Wien filter is similar to the one made by Kohashi [2], in which the iron yoke magnet is used. We use an iron free solenoid similar to Niimi’s Wien filter [13]. For the azimuthal rotation of spins, a round magnetic lens set at the image position of the first condenser lens similar to the one reported by Duden and Bauer [14] is used. Their spin rotator has electrostatic lenses for both sides of the rotator. In this investigation, double gap magnetic lenses are used, which can
Fig. 2. (a) Electron trajectory and magnetic and electrostatic field distribution of the beam selector. (b) Electric and magnetic field contour lines and beam shape exit from the beam selector.
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illuminated electrons hit the specimen at a few electron volts after retarding its energy. The reflected electrons from the specimen are accelerated to 10 or 20 keV by the accelerating lens. In the following, each component will be described in detail.
round under 20 kV accelerating voltage. It is possible to change the voltage until to get a round beam.
2.1. 908 deflection beam selector
To make the spin rotates to the perpendicular direction of the beam axis, it is necessary to apply the magnetic field perpendicular to the beam axis. Rotation angle of the spin is proportional to the excitation of the magnetic field. However, the perpendicular magnetic field acts to deflect the beam. In order to cancel the deflection of the beam, a Wien filter [4] is used. It consists of perpendicular magnetic and electrostatic fields normal to the beam axis. The deflection of the magnetic field is canceled by that of electrostatic field. Then, the beam axis is always straight after changing the spin rotation angle. It is necessary to put the image plane of the previous lenses at the center of the Wien filter. The spin polarized electron source works only under an extreme-high vacuum (EHV). The coils of the magnet must be placed outside the vacuum. Our spin rotator consists of a solenoid coil set outside the vacuum tube and a parallel plate electrode inside the vacuum. A cross-section of the system and the field distributions are shown in Fig. 3(a). When the accelerating voltage is 20 kV (or 10 kV), the excitation necessary to rotate 908 is
A 908 sector magnet is used as the beam selector of the SPLEEM. When the spin polarized beam is used, the beam selector is switched off. 45%Ni-Permalloy is used as the magnet yoke and pole-piece material to avoid a residual magnetic field. The beam selector is excited only when the LaB6 gun is used. Parallel beam enters into the beam selector as shown in Fig. 2. It is focused after exiting the sector magnet. A 908 sector magnet with parallel polepiece has a focusing effect only for the direction parallel to the pole-piece surface (X-direction). There is no focusing effect in the magnetic field direction normal to the pole-piece surface (Ydirection). A pair of electrodes is inserted inside the pole-piece gap to make a quadrupole electrostatic field combined with the magnet pole-pieces [15]. Astigmatism of the exit beam can be compensated by the electrode voltages. The magnetic field of 87.9 AT is applied to get 908 deflection and electrostatic quadrupole fields of Vx = 500 V and Vy = 500 V are applied to make the beam shape
2.2. Wien type spin manipulator
Fig. 3. (a) Contour lines of electrostatic potential and magnetic field vectors of the Wien type spin manipulator. (b) Electron beam trajectory in the Wien type spin manipulator. (c) Beam shape at the exit of the manipulator for a beam of 10,000 V and 9999 V. Slight dispersion has been observed.
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K. Tsuno et al. / Applied Surface Science 256 (2009) 1035–1041 Table 1 Comparison of the excitation of condenser lenses and spin rotator lenses before and after the 1808 rotation of spin at the accelerating voltage of 10 kV.
Fig. 4. Condenser lens system with a spin rotator and electron trajectory in those lenses.
182.16 AT (104.6 AT), the necessary Ampere-turn of each coil is 91.08 AT (or 52.3 AT). The straight beam focuses at the center of the Wien filter as shown in Fig. 3(b) under the Wien condition of V1 = 28.0 V and NI = 52.3 AT. Energy dispersion due to 1 eV energy spread of the beam makes the shape of the beam slightly blurred as shown in Fig. 3(c). 2.3. Spin rotation by a magnetic round lens Fig. 4 shows condenser lenses with a spin rotator lens for the azimuth control. There are three double gap magnetic lenses (condenser lenses: CL1, CL2 and CL3) and one single gap magnetic lens (spin rotator). It has been said that Duden has described in his Ph.D. thesis [Claustal 1996] similar condenser lens system. The first condenser lens (CL1) focuses the beam at the center of the gap of the spin rotator. Because the beam focuses at the gap center of the spin rotator, excitation change of the spin rotator from the 08 rotation to the 1808 rotation gives only a small change of the brightness. The relation between the demagnification of the condenser lens system and the first focus position Z1 is shown in Fig. 5. There are two lines. The one is the case where the spin rotation lens excitation is zero and the other is excited to rotate the spin 908. The center of the gap of the spin rotator lens is Z1 = 200 mm. Both curves coincide at Z1 = 200.3 mm. If the focus position deviates about 1 mm, the magnification difference becomes large. We have to adjust the CL1 focus position in order to stay the focus position the same after the excitation change of the spin rotator lens. Table 1 shows the comparison of the excitation of condenser lenses and spin rotator lenses before and after the 1808 rotation of spin at the accelerating voltage of 10 kV. After the 1808 rotation of the spin, the demagnification value inevitably changed. This must be corrected in each time and not so convenient to the operation. However, we can rotate the spin up to 1808. Sometimes, the balance of the excitations of the double gap lens is changed to help the spin rotation. If the excitations of the two coils are changed, it causes the lens principal plane and causes the condenser property largely.
Fig. 5. Magnification change after the rotation of the spin by exciting the single gap lens. There are two Z points: Z = 197 and Z = 200.3 mm, in which there are no magnification change after rotating spins. These points can be set by adjusting the strength of the first condenser lens CL1.
Spin rotation
08
1808
CL1 (AT) Spin rotator (AT) CL2 (AT) CL3 (AT) Magnification
475 0 2507.3 296.7 1/232.6
456.6 1685.4 2507.1 296.7 1/178.6
2.4. Condenser lens properties including the objective lens Fig. 6 shows a schematic diagram of the condenser lens system and the ray trajectory of the illumination beam system. The demagnification of CL1 (M1 = 0.25) cannot be set so small, because the crossover point of CL1 must be at the center of the spin rotation lens as shown in the previous section. The physical dimension of the spin rotator determines the crossover point. The second condenser lens CL2 largely demagnify (M1*M2 = 0.023769) the beam. The magnification of the third condenser lens CL3 is more than one and therefore the total magnification increases (M1*M2*M3 = 0.043571). The magnification increase is due to the existence of the beam separator (not shown in Fig. 6) between CL3 and OL and the focusing position of the CL3 is longer than the distance between the object of CL3. This causes a limitation in the LEEM condenser system. The large distance between CL3 and OL makes it difficult to change the beam size by adjusting the CL3. This is the second limitation of the condenser system of LEEM. However, the disadvantage can be overcome by the objective lens. The change of the beam size (brightness control) can be made by changing the voltage of the third electrode of the objective lens. LEEM uses a cathode lens as the objective lens. Cathode lens consists of a combined magnetic and electrostatic lenses or electrostatic lens only. The voltages of the electrostatic lens of our objective lens are as follows: V1 (bottom electrode) = 20 kV (or10 kV accelerating voltage), V2 (the magnet yoke) = variable, V3 (the magnet pole piece) = 20 kV and V4 (exit electron voltage from the specimen) = 1 or a few eV. We can use V2 for controlling the illumination condition of the system. If we change V2, focusing condition of the image forming lens system also changes. However, we can set a few fixed voltages of V2 such as (1) low magnification and wide illumination mode and (2) high magnification and narrow illumination area mode. It is not possible to have various modes in objective lens of TEM, because TEM has no electrostatic lens. However, in LEEM, low accelerating voltage (from a few kilo volts to a few ten kilo volts) enables to use the electrostatic objective lens and this makes it possible to use the variety modes. We can overcome the limitations of the condenser lenses by the use of the electrostatic objective
Fig. 6. Configuration of the condenser lens system with the objective lens (OL) and the ray path from the source to the specimen.
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Fig. 7. Image forming system of SPLEEM. (A) Objective lens, (B) double beam separator with 458 deflection angle, (C) mirror aberration corrector, (D) intermediate lenses, (E) hemispherical analyzer, and (F) projector lenses and detector. The first beam separator faces to the objective lens and the second separator to the mirror aberration corrector.
lens. The illumination area can be changed by adjusting the voltage of the objective lens.
the sector magnet. Both of b2 and b3 components can be created with the one dodecapole by superimposing both field components.
3. Optical properties of the beam separator
4. Objective lens and mirror aberration corrector
Fig. 7 shows a schematic diagram and ray trajectories of the beam separator together with the objective lens, mirror corrector and image forming lens system with the hemispherical analyzer. A round beam exited by the objective lens enters into the left side of the separator 1 and exits at 458 direction. The beam enters into the beam separator 2 and then exits at the bottom of the mirror corrector. Two multipole correctors are set at the entrance and the exit of the beam separator to compensate the astigmatism and the second order aberrations generated by the beam separator. Quadrupole magnetic field b2 and hexapole magnetic field b3 are created by dodecapole shape correctors 1 and 2. The field contour lines of the dodecapoles creating the quadrupole and hexapole fields are shown in Fig. 8. Quadrupole field is used to cancel the astigmatism and the hexapole field compensates the second order geometrical aberrations made by
The schematic view of the image forming system of the SPLEEM is shown in Fig. 7. It consists of an objective lens, a beam separator, a mirror aberration corrector, intermediate lenses, a hemispherical analyzer, projector lenses and a detector. After analyzing the objective lens and mirror corrector independently, the combined aberration properties of objective lens and the mirror corrector is discussed on the straight optical axis omitting the existence of the beam separator. Hemispherical electrostatic analyzer is put between the image forming lenses. However, image forming lenses and the analyzer will be descried in a coming paper. 4.1. Objective lens image forming properties Slightly different objective lenses are shown in Figs. 6 and 7 (or Fig. 10). The former lens (Fig. 6), which is studied by Chmelik et al. [16], has three voltages. In this case, the magnetic yoke (third
Fig. 8. Quadrupole (b2) and hexapole (b3) field contour lines created by a dodecapole corrector.
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electrode) voltage V3 is the same as the earth potential. The second electrode voltage V2 (magnetic pole piece facing to the specimen) can be changed. The first electrode V1 is the specimen. The latter lens (Fig. 7 or Fig. 10) has four voltages. We have analyzed both cases but discuss the four voltage one in the following. There are three electrodes (V2–V4) and the specimen is floating on a different voltage (V1). In this case, V2 can be set at the maximum (earth potential) to accelerate electrons as early as possible to avoid the Coulomb interactions between electrons. The third electrode (magnet yoke) voltage V3 can be changed to adjust the illumination condition and aberration coefficients and the fourth electrode (non-magnetic electrode) voltage V4, which is inserted in the bore of the objective lens from the bottom, is set at the earth potential. Optical properties of the lens are: magnification M = 12.7, spherical aberration coefficient Cs = 13.8 mm (155.3 m) and axial chromatic aberration coefficient Cc = 9.1 mm (0.73 m) at the objective side (image side) are obtained under the condition of electrostatic lens of V1 = 1 V, V2 = 20 kV, V3 = 1964 V and V4 = 20 kV and the excitation of the coil NI = 1510.7 AT. Aberration coefficients are expressed both of objective and image sides. In usually, those coefficients are expressed on the objective plane. However, we are now interested in aberration correction by the mirror corrector. It is set after the objective lens. When we consider how much aberration should be generated by the mirror, we need to know the aberration coefficients of the objective lens at the image side, where the corrector is connected. That is the reason why the aberration coefficients on the image side are also shown. Because the magnification of the objective lens is about 10 times, Cs at the image side is 10,000 times bigger than that of objective side and Cc 100 times. 4.2. Properties of the electron mirror Optical properties of a mirror with four electrodes [see Fig. 10] have been calculated. Fig. 9(a) and (b) shows Cs and Cc for various electrode voltages Vm2 and Vm3 of the mirror (see Fig. 10). The
Fig. 9. Properties of four electrode mirror. (a) A relation between Cs and Cc. (b) and (c) Electrode voltage Vm3 dependence of Cs (b) and Cc (c) as a parameter of Vm2.
Fig. 10. Arrangement of the mirror (left) and the objective lens (right). The electron ray starts from the object plane, comes into the mirror, reflected at the mirror, first focuses at the same object plane and lastly focuses secondly at the image plane of the objective lens.
voltage V1 is used to focus the beam at Z = 150 mm from the first electrode (V1). The voltage V4 is fixed to the accelerating voltage of 20 kV. It has been known that, it is possible to control both of Cs and Cc by adjusting Vm2 and Vm3. From these graphs, we usually know voltages Vm2 and Vm3 of the mirror to compensate the objective lens Cs and Cc. However, values of Cs = 155.3 m and Cc = 0.73 m of our objective lens are two small compared to the other one’s value [9] such as Cs < 25 km and Cc < 70m. In our case, the necessary V2 and V3 values are smaller than their case. This indicates that our objective lens properties are good in itself even before the aberration correction. 4.3. Aberration correction by mirror Fig. 10 shows a schematic drawing of a system with the mirror and the objective lens [17]. In the actual machine, there is a beam separator between those two elements as shown in Fig. 7. However, once the beam separator is introduced, we have to analyze the optical properties under 3D environment. If we want to analyze the aberration coefficients in the system shown in Fig. 7, the first thing we need to analyze is the second order aberrations of the beam separator. We need the three-dimensional analysis of the beam trajectory and aberration integral. However, both of mirror and the objective lens are axially symmetric and create only the third order aberrations. So that, if we want to analyze how the mirror corrector compensate the objective lens aberrations, we need no second order aberrations created by the beam separator. This is the reason why we analyze the system omitting the beam separator as shown in Fig. 10. If we omit the separator, the beam axis becomes straight and we can analyze the aberrations under axially symmetric condition. The ray starts from the objective plane (at Z = 150 mm) of the mirror. The ray initially runs from the right to the left. After reflected at the mirror (at about Z = 3 mm), the reflected beam takes the same trajectory with the incident beam and focus at the same plane of Z = 150 mm. Electrons go through this plane and focus again at the objective plane of the objective lens. Electrons are decelerated just before the specimen in the retarding potential of the objective lens and landed on the specimen with a weak potential of a few electron volts. The electron trajectory is thus the opposite direction of the real world. However, it is no problem of the obtained trajectories and aberrations, which are not depend on the direction. After some iterations of calculation by changing the Vm2 and Vm3 of the mirror, we have reached Cs = 0.65 mm and Cc = 0.141 mm at the objective plane. The voltages of Vm2 and Vm3 of the mirror are around Vm2 = 10 kV and Vm3 = 6.5 kV. Those aberration values are 4.7 and 1.5% of the initial values. Cs and Cc values are not independently controlled in this time. Cc is smaller than the corresponding Cs to be
K. Tsuno et al. / Applied Surface Science 256 (2009) 1035–1041
corrected at the same time. In order to get smaller aberration coefficients, it is a method to re-design the objective lens with larger Cc and smaller Cs values. 5. Conclusion Electron optical simulation has been made on the new SPLEEM. The highly polarized spin gun and the small aberration coefficients made by the aberration correction are important to increase the brightness and spatial resolution of SPLEEM. Aberration corrected SPLEEM with high spin polarized electron source can be used to visualize various magnetic bulk materials for fundamental use. References [1] K. Tsuno, Rev. Solid State Sci. 2 (1988) 623–658. [2] R.P. Rerrier, S. McVitie, W.A.P. Nicholson, IEEE Trans. Magn. MAG-26 (1990) 1337. [3] T. Yamamoto, K. Tsuno, H. Nishizawa, in: G.W. Bailey (Ed.), 33rd Ann. Proc. EMSA, Las Vegas, Claitor Pub., Baton Rouge, LA, 1975, p. 32. [4] T. Kohashi, H. Matsuyama, K. Koike, Rev. Sci. Instrum. 66 (1995) 5537.
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[5] W. Swiech, G.H. Fecher, Ch. Ziethen, O. Schmidt, G. Scho¨nhense, K. Grzelakowski, C.M. Schneider, R. Fro¨mter, H.P. Oepen, J. Kirschner, J. Electron Spectrosc. Relat. Phenomena 84 (1997) 171. [6] E. Bauer, Spin-polarized low energy electron microscopy, in: H. Kronmueller, S. Parkin (Eds.), The Handbook of Magnetism Advanced Magnetic Materials, vol. 3, John Wiley & Sons, Chichester, 2007, p. 1470. [7] T. Kohashi, K. Motai, AMTC Lett. 1 (2008) 70. [8] E. Bauer, T. Duden, R. Zdyb, J. Phys. D: Appl. Phys. 35 (2002) 2327. [9] D. Preikszas, H. Rose, J. Electron Microsc. 1 (1997) 1. [10] D. Preikszas, P. Hartel, R. Spehr, H. Rose, EUREM 12, Brno, Czech Republic, (2000), p. 181. [11] N. Yamamoto, T. Nakanishi, A. Mano, Y. Nakagawa, S. Okumi, M. Yamamoto, T. Konomi, X. Jin, T. Ujihara, Y. Takeda, T. Ohshima, T. Saka, T. Kato, H. Horinaka, T. Yasue, T. Koshikawa, M. Kuwahara, J. Appl. Phys. 103 (2008) 4905. [12] X. Jin, N. Yamamoto, Y. Nakagawa, A. Mano, T. Kato, M. Tanioku, T. Ujihara, Y. Takeda, S. Okumi, M. Yamamoto, T. Nakanishi, T. Saka, H. Horinaka, T. Kato, T. Yasue, T. Koshikawa, Super-high brightness and high spin-polarization photocathode, Appl. Phys. Express. 1 (2008) 045002. [13] H. Niimi, M. Kato, T. Kawasaki, T. Miyamoto, S. Suzuki, W.-J. Chun, M. Kudo, N. Kawahara, M. Doi, K. Tsukamoto, K. Asakura, in: M. Altman, Y. Watanabe, T. Koshikawa (Eds.), LEEM/PEEM 5, Proceedings of the Fifth International Conference on LEEM/PEEM, Himeji, Japan, 15–19 October, vol. 601 (20), 2006, p. 4742 (Special Issue of Surface Science). [14] T. Duden, E. Bauer, Rev. Sci. Instrum. 66 (1995) 2861. [15] Grelakowski, Rev. Sci. Instrum. 67 (1996) 742. [16] J. Chmelik, L. Veneklasen, G. Marx, Optik 83 (1989) 155. [17] L. Wang, J. Rouse, E. Munro, H. Liu, X. Zhu, Optik 119 (2008) 90.
Contents lists available at ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Design of a mirror aberration corrector and a beam separator for LEEM K. Tsuno a,b,*, T. Yasue a, T. Koshikawa a a b
Fundamental Electronics Research Institute, Osaka Electro-Communication Univ., Japan Electron Optics Solutions Tsuno, Japan
A R T I C L E I N F O
A B S T R A C T
Article history: Available online 6 June 2009
A SPLEEM (spin polarized low energy electron microscope) has been designed with a numerical simulation of electrostatic and magnetic field distributions and electron ray trajectories. Highly (more than 90%) spin polarized electron source has been used. A Wien type spin manipulator and a magnetic lens type spin rotator are used to align spin direction. A magnetic field free objective lens is designed to observe magnetic domain structure of magnetic materials. High or low magnification mode can be selected by using a combined electrostatic and magnetic objective lens for a high spatial resolution and a wide imaging area observation. An electrostatic mirror aberration corrector is installed after the image forming objective lens. A double deflection 458 beam separator is used to bend the direction of electrons from the source to the objective lens and from the objective lens to the mirror aberration corrector. ß 2009 Elsevier B.V. All rights reserved.
PACS: 41.85.Gy, 41.85.Lc Keywords: LEEM, SPLEEM, Mirror corrector, Beam separator, Cathode lens
1. Introduction Lorentz microscopy is a popular magnetic domain observation method with a transmission electron microscope (TEM/STEM). A drawback of Lorentz microscopy is its necessity of thin film specimen. It is well known that magnetic domain structure depends largely on the specimen shape. Bulk specimens can be observed in SEM and LEEM/PEEM. The origin of Type-I and Type-II magnetic contrast of SEM [1] is the Lorentz force. Type-I magnetic contrast uses leakage fields above the specimen similar to AFM. Type-II magnetic contrast in SEM has been used in practical magnetic materials such as a magnetic head [2] and a Si-steel. The former is used under the working frequencies and the latter is observed through the insulating coating [3]. The key technologies used are the lock-in amplifier in the former case and the high accelerating voltage in the latter case. Spin-SEM (or SEMPA) [4] does not use the Lorentz force. It analyzes the spin polarization ratio of the secondary electrons. PEEM with a circular polarized synchrotron radiation source [5] and spin polarized LEEM (SPLEEM) [6] are also the direct imaging bulk magnetic domain observation method. Among those methods, we shall compare two methods of Spin SEM and SPLEEM. 1. Vacuum: Spin SEM can be used lower vacuum than SPLEEM. 2. Objective lens: Spin SEM usually uses magnetic lens. However, SPLEEM can use totally electrostatic objective lens to avoid leakage magnetic field from the magnetic lens. 3.
* Corresponding author at: Electron Optics Solutions Tsuno 2-10-11, Mihori, Akishima, Tokyo 186-0001, Japan. Tel.: +81 42 544 9803; fax: +81 42 544 9803. E-mail address: [email protected] (K. Tsuno). 0169-4332/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2009.05.114
Detector: In spin SEM, detection system must be inserted at the gap between the objective lens and the specimen. This makes the working distance (WD) longer than the usual SEM and destroys the spatial resolution. In SPLEEM, nothing is necessary around the specimen. 4. Specimen: Spin SEM can be used in practical magnetic materials and has succeeded in observing 20 nm or less bit length of the recording media [7]. SPLEEM can be used exclusively for the specimens with a LEED pattern. It is hard to use the polycrystalline practical materials. 5. In situ observation: Spin SEM need a time to take a picture and not possible in using it under in situ condition. SPLEEM can be used in real time in principle. However, at present, it has only a low magnetic contrast due to the low spin polarization factor (about 20–30%) [8] and relatively low performance of LEEM prevent in situ observation. Although many advantages of SPLEEM in magnetic domain observation in principle, LEEM itself has various drawbacks compared to the other electron microscopes. Low spatial resolution is a typical example. In low magnification, fairly large area must be illuminated. On the other hand, at high magnifications, illumination area must be concentrated to get a bright image. However, in order to get a focused image in the image forming side, the objective lens must be used under the focused state. The same lens field is used both for the illumination and image forming objective lenses. This means that the objective lens condition is not perfect for the illumination. In the case of TEM, different regions of the objective lens field are used as the illumination and image forming lenses. The illumination field is weaker than that of the image forming field (conventional mode). Even if the condenser-objective condition (the same excitation fields between the illumination and the image forming region) is used, third condenser lens is added just
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Fig. 1. Electron beam illumination system. (A) Spin polarized electron source, (B) LaB6 electron source, (C) spin manipulator, (D) beam selector, (E) condenser lenses and spin rotator, and (F) beam separator and objective lens.
above the objective lens to spread out the illumination beam. However, the same third condenser lens cannot be put after the objective lens in LEEM, because there is a beam separator just after the objective lens. It is difficult to change the illumination area by the condenser lenses. This results either the low brightness at high magnification or a narrow illumination area in the low magnification. Relatively low spatial resolution of LEEM is a result of large aberrations of the objective lens and the large wave length of electrons due to the low accelerating voltage near the specimen. Aberration corrector has been attached to improve the resolution. A mirror corrector [9] has an axially symmetric structure and therefore suitable for the direct imaging microscopes. It needs a beam separator to separate the incident beam and the reflected beam. LEEM already has a beam separator between the illumination and image forming beams. Double beam separator has an advantage of cancelling the dispersion and the second order geometrical aberrations of the beam separator. By this reason, the mirror corrector is suitable for LEEM [10]. The present investigation focuses firstly on to improve the optical performance of LEEM. Optics of LEEM exists behind TEM and SEM. Experiences for designing TEM and SEM are applied to the design of a new LEEM to improve the performance of the condenser and objective lenses. Secondly, the LEEM is combined to the highly spin polarized electron source to make an SPLEEM. Spin manipulator design is also improved. Thirdly, simulation for a mirror aberration corrector has been made.
compensate the spin rotation, to enable higher accelerating voltages of 10–20 kV. Three double gap magnetic lenses are used to condense the illumination beam. The illumination area can be changed both by the second condenser lens (E in Fig. 1) and the objective lens (bottom right of F in Fig. 1). Beam separator (top left of F in Fig. 1) separates the direction of the illumination beam and the image forming beam. The objective lens consists of a cathode lens combined with the electrostatic and magnetic lenses. The
2. Illumination system Fig. 1 shows an illumination system of our SPLEEM. It has two electron guns; (1) a spin polarized electron gun (A in Fig. 1) and (2) a LaB6 gun (B in Fig. 1). The former consists of a strained superlattice thin film cathode based on GaAsP/GaAs semiconductor [11,12] and a pulsed laser beam which illuminates the cathode from the back of the film [11]. The selection of the gun is made by switching on (LaB6 gun) or off (spin gun) the 908 deflection beam selector (D of Fig. 1). Detailed spin polarization properties are described in reference [11]. A gun lens (the latter half of A: in Fig. 1) is used to make a parallel electron beam. There are two spin manipulators to rotate the electron spins into a plane perpendicular to the beam direction (C) and a rotation about the beam direction (E), respectively. The former spin manipulator made by a Wien filter is similar to the one made by Kohashi [2], in which the iron yoke magnet is used. We use an iron free solenoid similar to Niimi’s Wien filter [13]. For the azimuthal rotation of spins, a round magnetic lens set at the image position of the first condenser lens similar to the one reported by Duden and Bauer [14] is used. Their spin rotator has electrostatic lenses for both sides of the rotator. In this investigation, double gap magnetic lenses are used, which can
Fig. 2. (a) Electron trajectory and magnetic and electrostatic field distribution of the beam selector. (b) Electric and magnetic field contour lines and beam shape exit from the beam selector.
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illuminated electrons hit the specimen at a few electron volts after retarding its energy. The reflected electrons from the specimen are accelerated to 10 or 20 keV by the accelerating lens. In the following, each component will be described in detail.
round under 20 kV accelerating voltage. It is possible to change the voltage until to get a round beam.
2.1. 908 deflection beam selector
To make the spin rotates to the perpendicular direction of the beam axis, it is necessary to apply the magnetic field perpendicular to the beam axis. Rotation angle of the spin is proportional to the excitation of the magnetic field. However, the perpendicular magnetic field acts to deflect the beam. In order to cancel the deflection of the beam, a Wien filter [4] is used. It consists of perpendicular magnetic and electrostatic fields normal to the beam axis. The deflection of the magnetic field is canceled by that of electrostatic field. Then, the beam axis is always straight after changing the spin rotation angle. It is necessary to put the image plane of the previous lenses at the center of the Wien filter. The spin polarized electron source works only under an extreme-high vacuum (EHV). The coils of the magnet must be placed outside the vacuum. Our spin rotator consists of a solenoid coil set outside the vacuum tube and a parallel plate electrode inside the vacuum. A cross-section of the system and the field distributions are shown in Fig. 3(a). When the accelerating voltage is 20 kV (or 10 kV), the excitation necessary to rotate 908 is
A 908 sector magnet is used as the beam selector of the SPLEEM. When the spin polarized beam is used, the beam selector is switched off. 45%Ni-Permalloy is used as the magnet yoke and pole-piece material to avoid a residual magnetic field. The beam selector is excited only when the LaB6 gun is used. Parallel beam enters into the beam selector as shown in Fig. 2. It is focused after exiting the sector magnet. A 908 sector magnet with parallel polepiece has a focusing effect only for the direction parallel to the pole-piece surface (X-direction). There is no focusing effect in the magnetic field direction normal to the pole-piece surface (Ydirection). A pair of electrodes is inserted inside the pole-piece gap to make a quadrupole electrostatic field combined with the magnet pole-pieces [15]. Astigmatism of the exit beam can be compensated by the electrode voltages. The magnetic field of 87.9 AT is applied to get 908 deflection and electrostatic quadrupole fields of Vx = 500 V and Vy = 500 V are applied to make the beam shape
2.2. Wien type spin manipulator
Fig. 3. (a) Contour lines of electrostatic potential and magnetic field vectors of the Wien type spin manipulator. (b) Electron beam trajectory in the Wien type spin manipulator. (c) Beam shape at the exit of the manipulator for a beam of 10,000 V and 9999 V. Slight dispersion has been observed.
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K. Tsuno et al. / Applied Surface Science 256 (2009) 1035–1041 Table 1 Comparison of the excitation of condenser lenses and spin rotator lenses before and after the 1808 rotation of spin at the accelerating voltage of 10 kV.
Fig. 4. Condenser lens system with a spin rotator and electron trajectory in those lenses.
182.16 AT (104.6 AT), the necessary Ampere-turn of each coil is 91.08 AT (or 52.3 AT). The straight beam focuses at the center of the Wien filter as shown in Fig. 3(b) under the Wien condition of V1 = 28.0 V and NI = 52.3 AT. Energy dispersion due to 1 eV energy spread of the beam makes the shape of the beam slightly blurred as shown in Fig. 3(c). 2.3. Spin rotation by a magnetic round lens Fig. 4 shows condenser lenses with a spin rotator lens for the azimuth control. There are three double gap magnetic lenses (condenser lenses: CL1, CL2 and CL3) and one single gap magnetic lens (spin rotator). It has been said that Duden has described in his Ph.D. thesis [Claustal 1996] similar condenser lens system. The first condenser lens (CL1) focuses the beam at the center of the gap of the spin rotator. Because the beam focuses at the gap center of the spin rotator, excitation change of the spin rotator from the 08 rotation to the 1808 rotation gives only a small change of the brightness. The relation between the demagnification of the condenser lens system and the first focus position Z1 is shown in Fig. 5. There are two lines. The one is the case where the spin rotation lens excitation is zero and the other is excited to rotate the spin 908. The center of the gap of the spin rotator lens is Z1 = 200 mm. Both curves coincide at Z1 = 200.3 mm. If the focus position deviates about 1 mm, the magnification difference becomes large. We have to adjust the CL1 focus position in order to stay the focus position the same after the excitation change of the spin rotator lens. Table 1 shows the comparison of the excitation of condenser lenses and spin rotator lenses before and after the 1808 rotation of spin at the accelerating voltage of 10 kV. After the 1808 rotation of the spin, the demagnification value inevitably changed. This must be corrected in each time and not so convenient to the operation. However, we can rotate the spin up to 1808. Sometimes, the balance of the excitations of the double gap lens is changed to help the spin rotation. If the excitations of the two coils are changed, it causes the lens principal plane and causes the condenser property largely.
Fig. 5. Magnification change after the rotation of the spin by exciting the single gap lens. There are two Z points: Z = 197 and Z = 200.3 mm, in which there are no magnification change after rotating spins. These points can be set by adjusting the strength of the first condenser lens CL1.
Spin rotation
08
1808
CL1 (AT) Spin rotator (AT) CL2 (AT) CL3 (AT) Magnification
475 0 2507.3 296.7 1/232.6
456.6 1685.4 2507.1 296.7 1/178.6
2.4. Condenser lens properties including the objective lens Fig. 6 shows a schematic diagram of the condenser lens system and the ray trajectory of the illumination beam system. The demagnification of CL1 (M1 = 0.25) cannot be set so small, because the crossover point of CL1 must be at the center of the spin rotation lens as shown in the previous section. The physical dimension of the spin rotator determines the crossover point. The second condenser lens CL2 largely demagnify (M1*M2 = 0.023769) the beam. The magnification of the third condenser lens CL3 is more than one and therefore the total magnification increases (M1*M2*M3 = 0.043571). The magnification increase is due to the existence of the beam separator (not shown in Fig. 6) between CL3 and OL and the focusing position of the CL3 is longer than the distance between the object of CL3. This causes a limitation in the LEEM condenser system. The large distance between CL3 and OL makes it difficult to change the beam size by adjusting the CL3. This is the second limitation of the condenser system of LEEM. However, the disadvantage can be overcome by the objective lens. The change of the beam size (brightness control) can be made by changing the voltage of the third electrode of the objective lens. LEEM uses a cathode lens as the objective lens. Cathode lens consists of a combined magnetic and electrostatic lenses or electrostatic lens only. The voltages of the electrostatic lens of our objective lens are as follows: V1 (bottom electrode) = 20 kV (or10 kV accelerating voltage), V2 (the magnet yoke) = variable, V3 (the magnet pole piece) = 20 kV and V4 (exit electron voltage from the specimen) = 1 or a few eV. We can use V2 for controlling the illumination condition of the system. If we change V2, focusing condition of the image forming lens system also changes. However, we can set a few fixed voltages of V2 such as (1) low magnification and wide illumination mode and (2) high magnification and narrow illumination area mode. It is not possible to have various modes in objective lens of TEM, because TEM has no electrostatic lens. However, in LEEM, low accelerating voltage (from a few kilo volts to a few ten kilo volts) enables to use the electrostatic objective lens and this makes it possible to use the variety modes. We can overcome the limitations of the condenser lenses by the use of the electrostatic objective
Fig. 6. Configuration of the condenser lens system with the objective lens (OL) and the ray path from the source to the specimen.
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Fig. 7. Image forming system of SPLEEM. (A) Objective lens, (B) double beam separator with 458 deflection angle, (C) mirror aberration corrector, (D) intermediate lenses, (E) hemispherical analyzer, and (F) projector lenses and detector. The first beam separator faces to the objective lens and the second separator to the mirror aberration corrector.
lens. The illumination area can be changed by adjusting the voltage of the objective lens.
the sector magnet. Both of b2 and b3 components can be created with the one dodecapole by superimposing both field components.
3. Optical properties of the beam separator
4. Objective lens and mirror aberration corrector
Fig. 7 shows a schematic diagram and ray trajectories of the beam separator together with the objective lens, mirror corrector and image forming lens system with the hemispherical analyzer. A round beam exited by the objective lens enters into the left side of the separator 1 and exits at 458 direction. The beam enters into the beam separator 2 and then exits at the bottom of the mirror corrector. Two multipole correctors are set at the entrance and the exit of the beam separator to compensate the astigmatism and the second order aberrations generated by the beam separator. Quadrupole magnetic field b2 and hexapole magnetic field b3 are created by dodecapole shape correctors 1 and 2. The field contour lines of the dodecapoles creating the quadrupole and hexapole fields are shown in Fig. 8. Quadrupole field is used to cancel the astigmatism and the hexapole field compensates the second order geometrical aberrations made by
The schematic view of the image forming system of the SPLEEM is shown in Fig. 7. It consists of an objective lens, a beam separator, a mirror aberration corrector, intermediate lenses, a hemispherical analyzer, projector lenses and a detector. After analyzing the objective lens and mirror corrector independently, the combined aberration properties of objective lens and the mirror corrector is discussed on the straight optical axis omitting the existence of the beam separator. Hemispherical electrostatic analyzer is put between the image forming lenses. However, image forming lenses and the analyzer will be descried in a coming paper. 4.1. Objective lens image forming properties Slightly different objective lenses are shown in Figs. 6 and 7 (or Fig. 10). The former lens (Fig. 6), which is studied by Chmelik et al. [16], has three voltages. In this case, the magnetic yoke (third
Fig. 8. Quadrupole (b2) and hexapole (b3) field contour lines created by a dodecapole corrector.
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electrode) voltage V3 is the same as the earth potential. The second electrode voltage V2 (magnetic pole piece facing to the specimen) can be changed. The first electrode V1 is the specimen. The latter lens (Fig. 7 or Fig. 10) has four voltages. We have analyzed both cases but discuss the four voltage one in the following. There are three electrodes (V2–V4) and the specimen is floating on a different voltage (V1). In this case, V2 can be set at the maximum (earth potential) to accelerate electrons as early as possible to avoid the Coulomb interactions between electrons. The third electrode (magnet yoke) voltage V3 can be changed to adjust the illumination condition and aberration coefficients and the fourth electrode (non-magnetic electrode) voltage V4, which is inserted in the bore of the objective lens from the bottom, is set at the earth potential. Optical properties of the lens are: magnification M = 12.7, spherical aberration coefficient Cs = 13.8 mm (155.3 m) and axial chromatic aberration coefficient Cc = 9.1 mm (0.73 m) at the objective side (image side) are obtained under the condition of electrostatic lens of V1 = 1 V, V2 = 20 kV, V3 = 1964 V and V4 = 20 kV and the excitation of the coil NI = 1510.7 AT. Aberration coefficients are expressed both of objective and image sides. In usually, those coefficients are expressed on the objective plane. However, we are now interested in aberration correction by the mirror corrector. It is set after the objective lens. When we consider how much aberration should be generated by the mirror, we need to know the aberration coefficients of the objective lens at the image side, where the corrector is connected. That is the reason why the aberration coefficients on the image side are also shown. Because the magnification of the objective lens is about 10 times, Cs at the image side is 10,000 times bigger than that of objective side and Cc 100 times. 4.2. Properties of the electron mirror Optical properties of a mirror with four electrodes [see Fig. 10] have been calculated. Fig. 9(a) and (b) shows Cs and Cc for various electrode voltages Vm2 and Vm3 of the mirror (see Fig. 10). The
Fig. 9. Properties of four electrode mirror. (a) A relation between Cs and Cc. (b) and (c) Electrode voltage Vm3 dependence of Cs (b) and Cc (c) as a parameter of Vm2.
Fig. 10. Arrangement of the mirror (left) and the objective lens (right). The electron ray starts from the object plane, comes into the mirror, reflected at the mirror, first focuses at the same object plane and lastly focuses secondly at the image plane of the objective lens.
voltage V1 is used to focus the beam at Z = 150 mm from the first electrode (V1). The voltage V4 is fixed to the accelerating voltage of 20 kV. It has been known that, it is possible to control both of Cs and Cc by adjusting Vm2 and Vm3. From these graphs, we usually know voltages Vm2 and Vm3 of the mirror to compensate the objective lens Cs and Cc. However, values of Cs = 155.3 m and Cc = 0.73 m of our objective lens are two small compared to the other one’s value [9] such as Cs < 25 km and Cc < 70m. In our case, the necessary V2 and V3 values are smaller than their case. This indicates that our objective lens properties are good in itself even before the aberration correction. 4.3. Aberration correction by mirror Fig. 10 shows a schematic drawing of a system with the mirror and the objective lens [17]. In the actual machine, there is a beam separator between those two elements as shown in Fig. 7. However, once the beam separator is introduced, we have to analyze the optical properties under 3D environment. If we want to analyze the aberration coefficients in the system shown in Fig. 7, the first thing we need to analyze is the second order aberrations of the beam separator. We need the three-dimensional analysis of the beam trajectory and aberration integral. However, both of mirror and the objective lens are axially symmetric and create only the third order aberrations. So that, if we want to analyze how the mirror corrector compensate the objective lens aberrations, we need no second order aberrations created by the beam separator. This is the reason why we analyze the system omitting the beam separator as shown in Fig. 10. If we omit the separator, the beam axis becomes straight and we can analyze the aberrations under axially symmetric condition. The ray starts from the objective plane (at Z = 150 mm) of the mirror. The ray initially runs from the right to the left. After reflected at the mirror (at about Z = 3 mm), the reflected beam takes the same trajectory with the incident beam and focus at the same plane of Z = 150 mm. Electrons go through this plane and focus again at the objective plane of the objective lens. Electrons are decelerated just before the specimen in the retarding potential of the objective lens and landed on the specimen with a weak potential of a few electron volts. The electron trajectory is thus the opposite direction of the real world. However, it is no problem of the obtained trajectories and aberrations, which are not depend on the direction. After some iterations of calculation by changing the Vm2 and Vm3 of the mirror, we have reached Cs = 0.65 mm and Cc = 0.141 mm at the objective plane. The voltages of Vm2 and Vm3 of the mirror are around Vm2 = 10 kV and Vm3 = 6.5 kV. Those aberration values are 4.7 and 1.5% of the initial values. Cs and Cc values are not independently controlled in this time. Cc is smaller than the corresponding Cs to be
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corrected at the same time. In order to get smaller aberration coefficients, it is a method to re-design the objective lens with larger Cc and smaller Cs values. 5. Conclusion Electron optical simulation has been made on the new SPLEEM. The highly polarized spin gun and the small aberration coefficients made by the aberration correction are important to increase the brightness and spatial resolution of SPLEEM. Aberration corrected SPLEEM with high spin polarized electron source can be used to visualize various magnetic bulk materials for fundamental use. References [1] K. Tsuno, Rev. Solid State Sci. 2 (1988) 623–658. [2] R.P. Rerrier, S. McVitie, W.A.P. Nicholson, IEEE Trans. Magn. MAG-26 (1990) 1337. [3] T. Yamamoto, K. Tsuno, H. Nishizawa, in: G.W. Bailey (Ed.), 33rd Ann. Proc. EMSA, Las Vegas, Claitor Pub., Baton Rouge, LA, 1975, p. 32. [4] T. Kohashi, H. Matsuyama, K. Koike, Rev. Sci. Instrum. 66 (1995) 5537.
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