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 mic-

roprobes in the Institute of Nuclear Physics in Cracow (Poland) and in the Institute of Applied Physics in Sumy (Uk-

raine). 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 acomplicated instrument based on a small acceler-ator and a high energy (MeV) ion focusing system(FS). There are about 60 operating MPs in theworld. MPs are widely used in such areas as elec-tronics, biology, medicine, environment, geology,science materials, arts and archaeology.

At present MPs are operated in two modes [1]:the old mode involving elemental analysis byPIXE/RBS/FRS with a beam spot diameter (MPresolution) of 2±0.3 lm at a beam current of 100±1000 pA and the new mode permitting investiga-tions of many properties of matter by STIM/IBICwith spatial resolution of up to 20 nm at a currentof fA or single ions.

The FS is a rather long system with total lengthl>6 m. As it has been shown earlier [2,3], a shortversion of optimized FS (l� 2.3 m) based on adivided Russian quadruplet of magnetic quadru-pole lenses allows operation with submicron res-olutions. The short FSs have some advantages:they are compact and less sensitive to mechanicalvibrations as compared with long systems. More-over, the short FSs permit a considerable decreasein the limitation in the resolution due to gas scat-tering. The short FS has great promise for the nextgeneration of MP [4].

The MP in Sumy is based on a compact Van deGraa� accelerator with proton beam energy up to2 MeV [5]. It was planned to use a divided tripletof magnetic quadrupole lenses with a large de-magni®cation D (D>30) as an FS of the MP [6,7].This FS would provide only one (new) mode ofMP operation, but with an exceptionally highspatial resolution (up to 6 nm). In this case the MP

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

1 Tel.: +380-542-327087; fax: 48126371881; e-mail: suny@-

bron.ifj.edu.pl and iapuas@gluk.apc.org

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

operation in the conventional (old) mode wouldhave led to a considerable broading of the beamspot size on the target owing to strong lens aber-rations.

The objective of this paper is to demonstratethe possibilities of the novel optimized short FSsbased on a divided triplet or Russian quadruplet ofmagnetic quadrupole lenses (with compromisedD�15) to operate successful in the above men-tioned two MP modes.

2. Formulation of the problem

Unlike in Refs. [2±4,6±8], here calculations areperformed for the FSs based on divided triplet (Tsystem) and Russian quadruplet (Q system) mag-netic quadrupole lenses. It is to be noted that onlyFSs with equal (in x, y directions) values of thefactor demagni®cation (jDxj � jDy j) are consid-ered. These FSs allow a microbeam to be formedusing high quality circular metallic apertures. Sets

Table 1

Physical parameters of optimal systemsa

System Q T

Total length l (cm) 225 325

E�ective quadrupole length L (cm) 6.4 6.4

Bore radius (cm) 0.635 0.635

Object distance a (cm) 70 117.5

Working distance g (cm) 15 15

Quad. ®eld B1 (T) ÿ0.28 0.0474

Quad. ®eld B2 (T) 0.19 ÿ0.177

Quad. ®eld B3 (T) ÿ0.19 0.267

Quad. ®eld B4 (T) 0.28 ÿProton energy W (MeV) 2.5 2.5

Demagni®cation (dimensionless)

Dx 14 14

Dy 14.4 ÿ14.8

Chromatic aberration (lm/mrad/%)

hx=Hdi ÿ44 ÿ34

hy=/di ÿ193 175

Spherical aberration (lm/mrad3)

hx=H3i 2 2

hx=H2/2i 13 14

hy=H2/i 13 ÿ61

hy=/3i 64 ÿ14

Selected reduced parasitic sextupole aberration coe�cients (m/rad2/%)

hx=/2S2i ÿ ÿ63

hy=/HS2i ÿ 123

hx=H2S3i ÿ ÿ23

hx=/2S3i ÿ58 20

hy=/HS3i ÿ116 ÿ33

hy=/HS4i 31 ÿhx=H2S4i ÿ22 ÿhx=/2S4i 19 ÿ

Selected reduced parasitic octupole aberration coe�cients (lm/mrad3/%)

hy=/3O2i ÿ ÿ327

hx=H/2O2i ÿ ÿ47

hy=/H2O2i ÿ 46

hy=/3O3i 335 ÿhx=H/2O3i � hy=/H2O3i ÿ42 ÿ

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

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

of these apertures are manufactured by well-known ®rms as parts for electron microscopes.

The present paper is devoted to the secondoptimizing approach to FSs [2]. To optimize theFS means to minimize the beam spot size on thetarget for a given emittance (E) of the enteringbeam:

E � 16�r1H�2; �1�where r1 is the radius of the object aperture (m)and H is the beam divergence (half angle) behindthe object slit (rad).

The following parameters are given (see Table 1and Fig. 1):

dimensions of the lenses,distance (s) between lenses in the doublet,working distance (g),brightness of the ion source (b),

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, wherei � 1; . . . ; 4).

3. Results of the calculations

The numerical calculations are performed usingPRAM [9] and TRANSPORT [10] codes. UnlikeRef. [8] the calculations include all dominant lensaberrations (chromatic, spherical, sextupole andoctupole).

The beam spot diameter,

d � maxfdx; dyg; �2�was calculated as a function of the FS total lengthfor the above mentioned conditions. As it has beenshown [2], this function has a ¯at minimum. Sim-ilarly, there is a minimum at total length of 2.25and 3.25 m for Q and T systems, respectively, inour case. The calculated results are listed in Table1 and in Figs. 2 and 3.

The value of I can be determined from theformula [9,11]

I � E � b � W ; �3�

Fig. 1. Dimensions of the quadruplet (Q) and triplet (T) sys-

tems (see also Table 1).

Fig. 2. Beam envelopes along the ion path for the solutions Q

and T (see Table 1).

S. Lebed / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 145±149 147

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 ofthe beam (A mÿ2 radÿ2 eVÿ1) and W the beamenergy (eV).

The accelerators in Sumy and in Cracow allowthe microprobe operation with b� 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 havea su�ciently large and symmetric factor demag-ni®cation (jDxj � jDy j � 14) and small lens (in-trinsic and parasitic) aberrations. It opens thepossibility for the MPs to operate successfully inthe old mode with a resolution of about 1.5±2 lm(see Fig. 3) as well as in the new mode with spatialresolution of about 70 nm (at r1� 0.5 lm). Be-sides, circular apertures may be used both as ob-ject slit and angular collimator. Fig. 2 shows thatthe maximum deviation of the microbeam takesplace in the second lens for the T system and in thethird lens for the Q system. This is the reason forthe maximum e�ect of the aberrations in these

lenses leading to beam spot broadening on thetarget (see Fig. 3 and Table 1). Note also that di-vided T and Q systems have one and two inter-mediate crossovers, respectively (see Fig. 2). Thesystem T has positive Dx and negative Dy . Thesystem Q has positive Dx and positive Dy ( seeTable 1).

Contemporary MP quadrupole lenses havefairly low values of the parasitic ®eld components(0.05±0.3%) [14,15].

Fig. 3 shows that the Q and T systems allow theMP to operate in the old mode with an almostcircular beam spot at the target even with ratherlarge parasitic sextupole and octupole pole tip ®eldcontamination (0.5%) in the lenses.

5. Conclusion

Novel optimized short (l<3.5 m) FSs based ona divided triplet or Russian quadruplet of mag-netic quadrupole lenses are found. These systemspermit a considerable decrease in the limitation inthe resolution due to the intrinsic (chromatic andspherical) and main parasitic (sextupole and octu-pole) lens aberrations. The T and Q systems (with

Fig. 3. Proton beam spot at the target, calculated for the Q and T systems at W� 2.5 MeV, d� 0.05%, r1� 10 lm and H� 0.08 mrad

with 0.5% sextupole and octupole components included in all lenses.

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

symmetric and compromised jDxj � jDy j � 14)could provide fairly high MP resolutions in the oldmode (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 10lm and H 6 0.08 mrad) and even with rather largeparasitic (0.5%) lens aberrations. Note also thatthese systems proposed are simpler and less ex-pensive to manufacture, than those mentionedabove [4,6,7].

The Q system is being tested experimentally inthe Cracow MP now. It is planned to check the Tsystem in the Sumy MP in near future. The T andQ systems are greatly promising for the next gen-eration of compact and vertical MPs. The verticalMP would allow studies of biological samplesunder normal (atmospherical) conditions [16,17].

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