Development of imaging energy analyzer using multipole Wien filter

Applied Surface Science 241 (2005) 131–134 www.elsevier.com/locate/apsusc

Development of imaging energy analyzer using multipole Wien filter H. Niimia,
, M. Katob, T. Tsutsumia, T. Kawasakia, H. Matsudairaa, S. Suzukia, W.-J. Chuna,c, Y. Kitajimad, M. Kudob, K. Asakuraa a

Catalysis Research Center, Hokkaido University, 21-10 Kita, Kita-ku, Sapporo 001-0021, Japan b JEOL Ltd., 3-1-2 Musashino, Akishima, Tokyo 196-8558, Japan c Core Research for Evolutional Science and Technology, Japan Science and Technology Corporation, Japan d Photon Factory, Institute of Materials Structure Science, Tsukuba 305-0801, Japan Available online 11 November 2004

Abstract We discussed a new design of a Wien filter energy analyzer for an energy-filtered X-ray photoemission electron microscopy system. We have demonstrated that the second-order aberration and the third-order aperture aberration can be corrected by the multipole Wien filter by adjusting multipole components of electric and magnetic fields up to octupole components. The threedimensional charge simulation method indicated that 12 electrodes and magnetic poles can effectively reproduce these ideal electric and magnetic fields. # 2004 Elsevier B.V. All rights reserved. PACS: 07.78.+s; 29.30.Dn; 42.15.Frd Keywords: XPEEM; Wien filter; Multipole; Aberration correction

1. Introduction To clarify reaction processes at surface, it is important to identify the chemical species and their distribution on a mesoscopic scale. Microspectroscopy is one of the most suitable techniques to attain this purpose. EXPEEM is an abbreviation of energy


Corresponding author. Tel.: +81 11 706 9115; fax: +81 11 706 9115. E-mail address: [email protected] (H. Niimi).

filtered X-ray photoemission electron microscopy which is a combination of a photoemission electron microscopy (PEEM) and a X-ray photoelectron spectroscopy (XPS) [1–3]. The PEEM is a microscopy to image the surface distribution of the work function. Ertl and Rotermund have presented the surface spatiotemporal patterns during the CO oxidation reactions and revealed the reaction mechanisms [4]. The XPS is an electron spectroscopy which can provide the surface chemical species and their chemical state by analyzing the photoelectron kinetic

0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.09.086

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H. Niimi et al. / Applied Surface Science 241 (2005) 131–134

energies. Thus the simple combination of the two may bring us the EXPEEM. However, it is not a simple story. In the XPS, a hemispherical electrostatic energy analyzer is often used but its electron optical axis is curved. This curved optical axis is a disadvantage against the easy adjustment of the imaging conditions and the easy operation of the system. We are now developing a Wien filter-type energy analyzer with a straight optical axis. We have published the first EXPEEM image using the Wien filter type energy analyzer and X-rays with its energy more than 1000 eV [3]. One drawback of our Wien filter type energy analyzer is its low transmittance for photoelectrons since the Wien filter uses magnetic poles with cores which occupy the large area of the energy analyzer and reduce the acceptance angle of photoelectrons. We have designed a new type of Wien filter analyzer in which the bore size has been enlarged by installing the coreless magnets to allow the electrons to enter in a large acceptance angle. However, the large acceptance angle of the Wien filter will bring the ill effects of the aberrations. Accordingly the higher order aberration corrections are required to attain a good spatial and energy resolutions. In the hemispherical energy analyzer, it is not easy to reduce the higher order aberrations. The advantage of the Wien filter is the possibility to perform the higher order aberration corrections by using a multipole electrodes and magnetic poles. The purpose of this paper is to estimate the transmittance and the energy resolution of the aberration-corrected multipole Wien filter and to determine the number of electrodes and magnetic poles.

2. Parameters of aberration corrections The Wien filter selects the electron with a certain kinetic energy based on the force balance between electrostatic and Lorentz forces perpendicularly applied to electrons [5]. The electric and magnetic fields in the Wien filter are given by the general solution of the Laplace equation [6]. Assuming that electric and magnetic fields are uniform along the optical axis (z-axis), the multipole expansion of electrostatic potential Fðx; yÞ and the magnetic scalar

potential Cðx; yÞ are written in Cartesian coordinates, respectively, Fðx; yÞ ¼ f0  E1 x  E2 ðx2  y2 Þ  E3 xðx2  3y2 Þ  E4 ðx4  6x2 y2  y4 Þ     ;

(1)

m0 Cðx; yÞ ¼ B1 y  B2 xy  B3 yð3x2  y2 Þ  B4 xyðx2  y2 Þ     ;

(2)

where f0 is the pass energy and E1 ; B1 ; E2 ; B2 ; E3 ; B3 and E4 ; B4 are dipole, quadrupole, hexapole and octupole component coefficients of electric and magnetic potentials, respectively. In order to satisfy the Wien and stigmatic conditions and to perform the high order aberration corrections, we have to set the multipole components of electric and magnetic fields to suitable values. Condition ‘A’ corresponds to the stigmatic condition. Rose suggested that condition ‘B’ must be fulfilled if one wants to eliminate the aberrations up to the second-order terms [5]. We adopted condition ‘C’ proposed by Kato [7]. Condition ‘C’ can eliminate the second-order and the third-order aperture aberrations. Since it is important that the spatial distribution of electric multipole components also coincides with that of magnetic multipole components in the region of the fringing fields, we assume that condition ‘C’ is also satisfied in the region of fringing fields in this calculation.

3. Results and discussion To examine how much the aberration is improved by the adjustments of electric and magnetic fields as shown in Table 1, we compared the aberration figures according to three conditions. The calculation conditions are as follows: f0 ¼ 100 eV;

L ¼ 430 mm;

0  a0  14 ;

ðx0 ; y0 Þ ¼ ð0; 0Þ ðmmÞ; where f0 ; L; a0 and ðx0 ; y0 Þ represent the pass energy, the filter length, the acceptance angle and the incident position, respectively. The aberration figures were obtained at the positions that correspond to the focus point. The aberration figures of conditions ‘A’, ‘B’ and ‘C’ in Table 1 are given in Fig. 1(a)–(c), respectively.

H. Niimi et al. / Applied Surface Science 241 (2005) 131–134

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Table 1 The conditions for Wien, stigmatic and higher order aberration correction e2 ¼ EE2 R1 0

A

B

C

Condition

0.250

1.000

1.000

Stigmatic

b2 ¼ BB2 R1 0

0

0.750

0.750

E R2 ¼ E3 1 0 B R2 ¼ E3 1 0 E R3 ¼ E4 1 0 B R3 ¼ E4 1 0

0

0.375

0.563

e3

0

0

0.188

0

0

0.180

0 b4 E1  v0 B1 ¼ 0

0

b3 e4

Aberration correction

0

R0 ¼ 2f0 =E1 is a Larmer radius of electron here.

Fig. 2. Energy resolution dependence on the acceptance angle with different conditions: (a) condition ‘A’, (b) condition ‘B’, (c) condition ‘C’ and (d) 12 electrodes and magnetic poles.

The energy dispersion direction is set to the x direction in the figures. Trajectories in the energy dispersion direction focus on optical axis. The Wien filter installed in the EXPEEM system in Ref. [3] has satisfied condition ‘A’. The aberration of x direction of condition ‘A’ is about 20 mm while that of condition ‘C’ is about 2 mm. Next, we compared the acceptance angle for the 1 eV energy resolution since the transmission T is proportional to the solid angle to accept electrons which is expressed as 1  cos a0 . The acceptance angle a0 is 2.5  for condition ‘A’ while 13  for condition ‘C’ from Fig. 2. Consequently it is expected that condition ‘C’ will provide 26 times brighter image than condition ‘A’ in the same energy resolution. The next calculation we have to carry out is how many electrodes and magnetic poles are necessary to simulate the ideal potentials for condition ‘C’ because the aberration figure in Fig. 1 is calculated on the ideal potentials and real potentials is formed by a finite number of discrete electrodes and magnets. We

calculated the aberration figure using the threedimensional charge simulation method (3D-CSM) with different numbers of electrodes and magnetic poles. Fig. 3(a)–(d) shows aberration figures of using 8, 10, 12 and 18 electrodes and magnetic poles. They are symmetrically arranged on the cylinder surface. The spreads of the aberration figures in the x direction of 8 and 10 electrodes and magnetic poles were about 20 and 15 mm, respectively, while those of 12 and 18 electrodes and magnetic poles were suppresses to 5 mm. Further calculation of 12 electrodes and magnetic poles showed that we could have the acceptance angle of 11  to attain the 1 eV energy resolution as shown in Fig. 2(d). This corresponds to 70% of the transmittance for the ideal case of condition ‘C’, which means the Wien filter with the 12 electrodes and magnetic poles will be 19 times brighter than the present Wien filter. No big difference in aberration figures was found between 12 and 18 electrodes and magnetic poles. Thus 12 electrodes and magnetic poles are a realistic solution to attain the

Wien

Fig. 1. Comparison of aberration figures given by parameters in Table 1. (a), (b) and (c) correspond to conditions ‘A’, ‘B’ and ‘C’, respectively. The horizontal axis corresponds to the energy dispersion direction.

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Fig. 3. Comparison of the aberration figure corresponding to the number of electrodes and magnetic poles: (a) 8 electrodes and magnetic poles, (b) 10 electrodes and magnetic poles, (c) 12 electrodes and magnetic poles and (d) 18 electrodes and magnetic poles. The horizontal axis corresponds to the energy dispersion direction.

aberration-corrected Wien filter based on the Kato’s condition ‘C’. We are now constructing a new multipole Wien filter and will soon check its performance.

aberrations effectively. This new type of multipole Wien filter will bring us a user-friendly and bright EXPEEM system.

4. Conclusion

References

We calculated electron trajectories in the multipole Wien filter to estimate the improvement of the transmittance by the aberration correction up to the third-order aperture aberration. As a result we have shown in the ideal electric and magnetic fields that the transmittance can be 26 times better than the Wien filter that we are using now. We also performed the numerical calculation to obtain necessary number of the electrodes and magnetic poles. We have shown that 12 electrodes and magnetic poles can correct

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