Optimized short focusing systems for a nuclear microprobe

Nuclear Instruments and Methods in Physics Research B 152 (1999) 145±149

Optimized short focusing systems for a nuclear microprobe S. Lebed

1

Applied Physics Institute, National Academy of Sciences of the Ukraine, 244030 Sumy, Ukraine Received 6 October 1998; received in revised form 8 December 1998

Abstract The paper describes short versions of optimized focusing systems based on a divided Russian quadruplet and a triplet of magnetic quadrupole lenses. The systems have a total length l < 3.5 m. The calculations include all dominant lens aberrations (chromatic, spherical, sextupole and octupole). The results are used to design new scanning nuclear microprobes in the Institute of Nuclear Physics in Cracow (Poland) and in the Institute of Applied Physics in Sumy (Ukraine). The expected resolutions of the microprobes are presented. The proposed systems are greatly promising for the next generation of compact and vertical microprobes. Ó 1999 Published by Elsevier Science B.V. All rights reserved.

1. Introduction The scanning nuclear microprobe (MP) is a complicated instrument based on a small accelerator and a high energy (MeV) ion focusing system (FS). There are about 60 operating MPs in the world. MPs are widely used in such areas as electronics, biology, medicine, environment, geology, science materials, arts and archaeology. At present MPs are operated in two modes [1]: the old mode involving elemental analysis by PIXE/RBS/FRS with a beam spot diameter (MP resolution) of 2±0.3 lm at a beam current of 100± 1000 pA and the new mode permitting investigations of many properties of matter by STIM/IBIC with spatial resolution of up to 20 nm at a current of fA or single ions. 1 Tel.: +380-542-327087; fax: 48126371881; e-mail: [email protected] and [email protected]

The FS is a rather long system with total length l > 6 m. As it has been shown earlier [2,3], a short version of optimized FS (l ˆ 2.3 m) based on a divided Russian quadruplet of magnetic quadrupole lenses allows operation with submicron resolutions. The short FSs have some advantages: they are compact and less sensitive to mechanical vibrations as compared with long systems. Moreover, the short FSs permit a considerable decrease in the limitation in the resolution due to gas scattering. The short FS has great promise for the next generation of MP [4]. The MP in Sumy is based on a compact Van de Graa€ accelerator with proton beam energy up to 2 MeV [5]. It was planned to use a divided triplet of magnetic quadrupole lenses with a large demagni®cation D (D > 30) as an FS of the MP [6,7]. This FS would provide only one (new) mode of MP operation, but with an exceptionally high spatial resolution (up to 6 nm). In this case the MP

0168-583X/99/$ ± see front matter Ó 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 9 7 8 - 1

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S. Lebed / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 145±149

operation in the conventional (old) mode would have led to a considerable broading of the beam spot size on the target owing to strong lens aberrations. The objective of this paper is to demonstrate the possibilities of the novel optimized short FSs based on a divided triplet or Russian quadruplet of magnetic quadrupole lenses (with compromised D  15) to operate successful in the above mentioned two MP modes.

2. Formulation of the problem Unlike in Refs. [2±4,6±8], here calculations are performed for the FSs based on divided triplet (T system) and Russian quadruplet (Q system) magnetic quadrupole lenses. It is to be noted that only FSs with equal (in x, y directions) values of the factor demagni®cation (jDx j  jDy j) are considered. These FSs allow a microbeam to be formed using high quality circular metallic apertures. Sets

Table 1 Physical parameters of optimal systemsa System Total length l (cm) E€ective quadrupole length L (cm) Bore radius (cm) Object distance a (cm) Working distance g (cm) Quad. ®eld B1 (T) Quad. ®eld B2 (T) Quad. ®eld B3 (T) Quad. ®eld B4 (T) Proton energy W (MeV) Demagni®cation (dimensionless) Dx Dy Chromatic aberration (lm/mrad/%) hx=Hdi hy=/di Spherical aberration (lm/mrad3 ) hx=H3 i hx=H2 /2 i hy=H2 /i hy=/3 i Selected reduced parasitic sextupole aberration coecients (m/rad2 /%) hx=/2 S2i hy=/HS2i hx=H2 S3i hx=/2 S3i hy=/HS3i hy=/HS4i hx=H2 S4i hx=/2 S4i Selected reduced parasitic octupole aberration coecients (lm/mrad3 /%) hy=/3 O2i hx=H/2 O2i hy=/H2 O2i hy=/3 O3i hx=H/2 O3i ˆ hy=/H2 O3i a

Q

T

225 6.4 0.635 70 15 ÿ0.28 0.19 ÿ0.19 0.28 2.5 14 14.4

325 6.4 0.635 117.5 15 0.0474 ÿ0.177 0.267 ÿ 2.5 14 ÿ14.8

ÿ44 ÿ193

ÿ34 175

2 13 13 64

2 14 ÿ61 ÿ14

ÿ ÿ ÿ ÿ58 ÿ116 31 ÿ22 19

ÿ63 123 ÿ23 20 ÿ33 ÿ ÿ ÿ

ÿ ÿ ÿ 335 ÿ42

ÿ327 ÿ47 46 ÿ ÿ

S2, O2, etc are for the % parasitic sextupole and octupole pole tip ®eld contamination, respectively, in quadrupole lens 2, etc.

S. Lebed / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 145±149

of these apertures are manufactured by wellknown ®rms as parts for electron microscopes. The present paper is devoted to the second optimizing approach to FSs [2]. To optimize the FS means to minimize the beam spot size on the target for a given emittance (E) of the entering beam: E ˆ 16…r1 H†2 ;

…1†

where r1 is the radius of the object aperture (m) and H is the beam divergence (half angle) behind the object slit (rad). The following parameters are given (see Table 1 and Fig. 1): dimensions of the lenses, distance (s) between lenses in the doublet, working distance (g), brightness of the ion source (b),

147

emittance (E) of the microbeam, proton energy (W) and momentum spread (d) of the protons in the beam. The following parameters are varied: FS total length (1 6 l 6 5 m), object distance (a), object slit diameters (1 6 d1 6 20 lm), lens excitations (0.1 6 ki 6 1.0, where i ˆ 1; . . . ; 4). 3. Results of the calculations The numerical calculations are performed using PRAM [9] and TRANSPORT [10] codes. Unlike Ref. [8] the calculations include all dominant lens aberrations (chromatic, spherical, sextupole and octupole). The beam spot diameter, d ˆ maxfdx ; dy g;

…2†

was calculated as a function of the FS total length for the above mentioned conditions. As it has been shown [2], this function has a ¯at minimum. Similarly, there is a minimum at total length of 2.25 and 3.25 m for Q and T systems, respectively, in our case. The calculated results are listed in Table 1 and in Figs. 2 and 3. The value of I can be determined from the formula [9,11] I ˆE
b
W;

Fig. 1. Dimensions of the quadruplet (Q) and triplet (T) systems (see also Table 1).

…3†

Fig. 2. Beam envelopes along the ion path for the solutions Q and T (see Table 1).

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S. Lebed / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 145±149

Fig. 3. Proton beam spot at the target, calculated for the Q and T systems at W ˆ 2.5 MeV, d ˆ 0.05%, r1 ˆ 10 lm and H ˆ 0.08 mrad with 0.5% sextupole and octupole components included in all lenses.

where I is an ion beam current on the specimen (A), E the phase volume (emittance) of the beam (m2 rad2 ), b the energy normalized brightness of the beam (A mÿ2 radÿ2 eVÿ1 ) and W the beam energy (eV). The accelerators in Sumy and in Cracow allow the microprobe operation with b ˆ 5±20 A mÿ2 radÿ2 eVÿ1 at H 6 0.1 mrad [2,5,11±13]. 4. Discussion As shown in Table 1, the systems Q and T have a suciently large and symmetric factor demagni®cation (jDx j  jDy j  14) and small lens (intrinsic and parasitic) aberrations. It opens the possibility for the MPs to operate successfully in the old mode with a resolution of about 1.5±2 lm (see Fig. 3) as well as in the new mode with spatial resolution of about 70 nm (at r1 ˆ 0.5 lm). Besides, circular apertures may be used both as object slit and angular collimator. Fig. 2 shows that the maximum deviation of the microbeam takes place in the second lens for the T system and in the third lens for the Q system. This is the reason for the maximum e€ect of the aberrations in these

lenses leading to beam spot broadening on the target (see Fig. 3 and Table 1). Note also that divided T and Q systems have one and two intermediate crossovers, respectively (see Fig. 2). The system T has positive Dx and negative Dy . The system Q has positive Dx and positive Dy ( see Table 1). Contemporary MP quadrupole lenses have fairly low values of the parasitic ®eld components (0.05±0.3%) [14,15]. Fig. 3 shows that the Q and T systems allow the MP to operate in the old mode with an almost circular beam spot at the target even with rather large parasitic sextupole and octupole pole tip ®eld contamination (0.5%) in the lenses. 5. Conclusion Novel optimized short (l < 3.5 m) FSs based on a divided triplet or Russian quadruplet of magnetic quadrupole lenses are found. These systems permit a considerable decrease in the limitation in the resolution due to the intrinsic (chromatic and spherical) and main parasitic (sextupole and octupole) lens aberrations. The T and Q systems (with

S. Lebed / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 145±149

symmetric and compromised jDx j  jDy j  14) could provide fairly high MP resolutions in the old mode (d  1:5±2 lm) as well as in the new mode (d  70 nm) under standard MP conditions (d  0.05%, b P 5 A mÿ2 radÿ2 eVÿ1 , 0.5 6 r1 6 10 lm and H 6 0.08 mrad) and even with rather large parasitic (0.5%) lens aberrations. Note also that these systems proposed are simpler and less expensive to manufacture, than those mentioned above [4,6,7]. The Q system is being tested experimentally in the Cracow MP now. It is planned to check the T system in the Sumy MP in near future. The T and Q systems are greatly promising for the next generation of compact and vertical MPs. The vertical MP would allow studies of biological samples under normal (atmospherical) conditions [16,17]. References [1] G. Legge, Nucl. Instr. and Meth. B 130 (1997) 9. [2] V. Brazhnik, S. Lebed, W. Kwiatek, Z. Stachura, M. Cholewa, D. Jamieson, G. Legge, Nucl. Instr. and Meth. B 130 (1997) 104. [3] V. Brazhnik, Z. Chioh, M. Cholewa, D. Jamieson, S. Lebed, G. Legge, A. Rys, Z. Stachura, Proceedings of XXXII Zakopane School of Physics, Poland, 1997, p. 357.

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[4] V. Brazhnik, A. Dymnikov, D. Jamieson, S. Lebed, G. Legge, A. Ponomarev, V. Storizhko, Nucl. Instr. and Meth. B 104 (1995) 92. [5] A. Vergunov, Yu. Levchenko, M. Novikov, V. Pistrjiak, V. Storizhko, S. Chekanov, Voprosi Atomnoj Nauki i Techniki (USSR), Ser.: Obschaja Fizika 3 (24) (1983) 13. [6] V. Brazhnik, V. Khomenko, S. Lebed, A. Ponomarev, Nucl. Instr. and Meth. B 104 (1995) 69. [7] V. Brazhnik, S. Lebed, Nucl. Instr. and Meth. B 130 (1997) 90. [8] V. Brazhnik, A. Dymnikov, R. Hellborg, S. Lebed, J. Pallon, V. Storizhko, Nucl. Instr. and Meth. B 77 (1993) 29. [9] M. Breese, D. Jamieson, P. King, Materials Analysis with a Nuclear Microprobe, Wiley, New York, 1996. [10] K.L. Brown, SLAC-91, 1977. [11] A. Kalinichenko, V. Khomenko, S. Lebed, S. Mordik, V. Voznij, Nucl. Instr. and Meth. B 22 (1997) 274. [12] D. Mous, R. Haitsma, T. Butz, R. Flagmeyer, D. Lehmann, J. Vogt, Nucl. Instr. and Meth. B 130 (1997) 31. [13] R. Szymanski, D. Jamieson, Nucl. Instr. and Meth. B 130 (1997) 80. [14] D. Jamieson, G. Legge, Nucl. Instr. and Meth. B 30 (1988) 235. [15] D. Jamieson, J. Zhu, Y. Mao, R. Lu, Z. Wang, J. Zhu, Nucl. Instr. and Meth. B 104 (1995) 86. [16] M. Folkard, B. Vojnovic, G. Schettino, M. Forsberg, G. Bowey, K. Prise, B. Michael, A. Michette, S. Pfauntsch, Nucl. Instr. and Meth. B 130 (1997) 270. [17] M. Cholewa, A. Saint, G. Legge, T. Kamiya, Nucl. Instr. and Meth. B 130 (1997) 275.