Some optimal focusing systems for a compact nuclear microprobe

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&

Nuclear Instruments

and Methods in Physics Research B 122

(1997)127- 132

NIOMI B

Boam Interactions with Materials 8 Atoms

ELSEVIER

Some optimal focusing systems for a compact nuclear microprobe V. Brazhnik, S. Lebed’ Applied Physics Institutr, Nutional Acudemy of Sciences of‘the Ukruine, 244030 &my, Ukraine Received

12 October

1995; revised form received 27 August 1996

Abstract We describe the numerical study of some short (I < 3.2 m> optima1 lens systems which consist of three magnetic quadrupole lenses suitable for using in a nuclear microprobe, taking into account chromatic and geometrical aberrations of the third order. We consider dependences of optimum emittance upon microprobe resolution and momentum spread. It is shown that the use of these focusing systems has great promises for use in compact nuclear microprobes with submicron resolutions.

1. Introduction

2. Numerical studies of the divided short FS with three magnetic quadrupole lenses

The existing microprobes (MP) with ion energy in the MeV range, which allow a submicron beam spot size on the target at a comparatively large beam current (I - 100 PA) to be obtained, are quite long constructions. The full lengths of their focusing systems (FS) consisting of three or more magnetic quadrupole lenses are more than four meters [ 1,2]. On the other hand, as it has been shown [3], there exist shorter (I = 3.19 m) optimized divided FS consisting of three magnetic quadrupole lenses which, provides resolutions of 0.01 pm ZGd 5 1 pm at higher values of FS maximum emittance compared with long (I= 7.45 m) traditional (TL) or divided (DL) systems. Besides, it has been calculated [4] that a similar short optimized FS (one triplet and four quadruplets) could provide much higher probe currents for main Melbourne’s MP techniques (PIXE, RBS, STIM, IBIC) when compared with experimental measurements on the traditional Russian quadruplet. The obtained results show that it is necessary to make more detailed numerical studies of FS with the total lengths less than 320 cm. Such studies are made in this paper. It is known [I,21 that existing MP with submicron resolutions are generally operated on the basis of ion accelerators with a momentum spread 8 I (l-5) X 10P2%. However, many laboratories, equipped with ion accelerators with 6 > 5 X lo-‘%, would like to know if it is possible and under which conditions to make MP (including also compact ones) with submicron resolution on the basis of such ion accelerators. The reply is given in this work.

2.1. Formulation

0168-583X/97/$17.00 Copyright /‘II SO168-583X(96)00652-0

of the task

Unlike in Ref. [3], here we have studied some shorter (I, = 319 cm, I, = 219 cm, I, = 119 cm) optimized FS in a wide range of the parameter 6 (0.001 5 6 5 0.25%). The following parameters are variable: Half-widths of rectangular object slit (rlrr rlY) and angular collimator (4, 13); Distance (A) between the first and the second lenses; Object distance (a); Excitations of the lenses (k,, k,, k,). The following parameters are given: Effective lengths of the lenses (L = L, = .Z,, = L,); Working distance (g); Bore radii (r,) of the lenses; Proton energy and momentum spread of the beam. In this case the phase volume (emittance) of the FS beam entering may be written as E = 16r,,r,,@.

(1)

In this paper we suppose that the brightness of the ion source B is some given value for the considered MP. In this case the ion beam current on the target is proportional to E, and the maximum value of the emittance (E * ) at a given beam size on the target(d) determines the maximum beam current on the target. For each value pair of the variable parameters a, h, the parameter values rlr, rlY, 8, $J which provide the value E * and satisfy the equalities have been found: d., = d,

0 1997 Elsevier Science B.V. All rights reserved

d, = d,

(2)

128

V. Bruzhnik. S. Lebed’/Nucl.

Instr. and Meth.

where d, and d, are the beam spot sizes on the target taking into account the chromatic and spherical aberrations. The values of d,, d, were calculated by solving equations of motion for N beam particles of a phase range whose volume is determined by formula (1). In this paper N = 625. Taking into account technological reasons, suppose that all FS have the same working distance and all three lenses have the same effective lengths and the same bore radii (Table I).

Table I The physical parameters

in Phys. Res. B 122 (1997) 127-132

Here, like in Ref. [3], we consider FS in the real ranges of parameters (r, 2 0.5 pm, k I 1, S 2 0.001%). 2.2. Calculation results Ion-optical parameters of three optimized short divided systemsDS(I=319cm),DSl(I=219cm),DS2(1= 119 cm) are tabulated in Table 1. In Tables 2 and 3 the way of getting necessary MP resolutions at the corresponding values of the beam emittance is shown due to the systems DSI, DS2 changing the parameters of the object slit and

of optimal systems

Triplet systems

DS

DSI

DS2

Total length 1 km)

319.0

219.0

119.0

Effective quad. lengths (cm) Object distance CI(cm) Drift spaces (cm) Drift space x (cm) Working distance g km)

5.0 196.0 89.0 4.0 15.0

5.0 145.0 42.0 2.0 15.0

5.0 50.0 38.0 1.0 15.0

Excitations of quad. (dimensionless) k, k, k,

0.6570808985 0.6570808985 0.7833856919

0.7648291038 0.7648291038 0.8618687166

0.8 194309874 0.8 194309874 0.9062458660

Demagnifications DX DY

133.4 - 42.5

64.2 - 24.3

20.7 - 10.1

Chromatic aberration ( pm/mrad%) Cx/OS > (Y/e@)

- 200 1223

- 107 767

-33 322

Spherical aberration ( pm/mrad3) (x/e,) (x/e&‘) ( Y/e24>

1712 1619 - 5077 - 1705

261 368 - 972 - 420

IO 25 -51 -32

2.88E - 2

2.85E - 2

1.54E - 2

8.8941 1.7171

4.5365 0.8984

1.6018 0.7277

Optimum emittance ( pm2 mrad2)

E*

Object slit (pm) ‘I I rtp Angles of the beam after object slit (mrad) :

0.004011 0.029408

0.006915 0.063 192

0.006833 0.120956

Beam size on the target d(@m)

0.2

0.2

0.2

Momentum spread s (%) Quad. field B, CT) Quad. field B, CT) Quad. field B, (T) Bore radius km) Proton energy (MeV)

0.0 I 0.28 1277 0.281277 0.399805 0.65 3

0.01 0.381088 0.381088 0.483926 0.65 3

0.0 1 0.437443 0.437443 0.535043 0.65 3

V. Brazhnik, S. Lebed’/Nucl.

Instr. and Meth. in Phys. Res. B 122 (1997) 127-132

129

Table 2 The way of getting necessary MP resolutions at corresponding values of optimal emittance due to the system DS 1 changing parameters of object slit and angular collimator is shown DSl System d(pm)

rlx (crm)

rIV (pm)

0 (mrad)

do(mrad)

E ( ym’mrad*)

1.00 0.80 0.60 0.40 0.30 0.20 0.16 0.10

28.7618 22.8770 16.7662 10.8832 7.5394 4.5365 3.3839 1.4391

5.3908 4.4349 3.283 1 2.3084 1.9664 0.8984 0.8344 0.5366

0.0219 0.0226 0.0265 0.0229 0.0345 0.0632 0.0287 0.0356

0.0283 0.0225 0.0174 0.0114 0.0071 0.0692 0.0052 0.0032

1.54E-00 8.26E - 01 4.06E - 0 I 1.05E - 01 5.77E - 02 2.858 - 02 6.77E - 03 14OE-03

angular collimator. The dependence of the beam emittance on the beam spot size (Fig. 1) was constructed, respectively, on the basis of Tables 2 and 3 and data taken from Ref. [3]. Table 1 shows that the DSl and DS2 systems like the DS system allow a d = 0.2 pm resolution at 6 = 0.01% to be obtained in spite of the fact that they have smaller demagnifications. This is the result of the smaller chromatic and spherical aberrations of the DSl and DS2 systems than those of the DS system. At the same time the

half-widths (r, +, r,r) of the object slit and angular collimator (4, 6) of the DSl and DS2 systems have to be reduced. This naturally leads to a decrease of the optimal emittance, especially for the DS2 system (Fig. 1). Fig. 1 shows that the shorter DSl system has some advantage over the DS system at d = 0.2 pm. At the same time the longer DSl system exceeds the DS2 system in the parameter E’ (rlxr rlY, 4, 0) at d 2 0.2 pm. But at d = 0.16 pm and 6= 0.01% the DS2 system is more effective in the parameter E * than the DS 1 system. It is

Table 3 The way of getting necessary MP resolutions at corresponding values of optimal emittance due to the system DS2 changing parameters of object slit and angular collimator is shown DS2 System d(prn)

rlx (pm)

*ry (pm)

9 (mrad)

do(mmd)

E (~m*mrad*)

I .oo

9.742 1 7.7050 5.3517 3.6315 2.6253 1.6018 1.1832

4.3245 3.4967 2.5820

0.1976 0.1958 0.2175 0.1828 0.1674 0.1210 0.1159

0.0070 0.0049 0.0046 0.0039 0.0053 0.0068 0.0070

9.32E - 01 4.1lE-01 2.19E - 01 7.14E - 02 4.6OE - 02 1.54E - 02 8.21E - 03

0.80 0.60 0.40 0.30 0.20 0.16

1.7202 I .2239 0.7277 0.5382

Table 4 The way of getting necessary MP resolution (d = 0.4 pm) at corresponding values of parameter 6 and optimal emittance due to the system DS changing the parameters of the object slit and angular collimator is shown DS System (d = 0.4 Fm> s (o/o)

rlA (pm)

rlY (pm)

6 (mrad)

4 (mrad)

E (pm* mrad*)

0.001 0.010 0.020 0.040 0.060 0.100 0.150

18.9581 20.2576 12.9188 3.7079 3.9339 3.8129 3.7414

5.3718 2.9411 2.5323 1.7142 1.5189 1.2915 0.9793

0.03 19 0.0325 0.0282 0.0218 0.0125 0.0067 0.0038

0.0097 0.0061 0.0038 0.0023 0.0014 0.0007 0.0005

5.03E 1.88E 5.6OE 5.15E 1.73E 3.80E 1.04E-

01 01 02 03 03 04 04

V. Bruzhnik.

I

A

-DS

0 +

-DSl -DS2

S. Lebed’ /Nucl.

Instr. und Meth. in Phys. Rc.5. B I22 (1997) 127-132

A . DS . DS

6 =&of%

,I=319cm. ,I=3wcm,

d=o.*p In, d=o.lprn)

q - DSl (I=7.lScm, d=O.Sp m)

. -

I

. DSI (CZlScm, d=O.lp m) +- DSZ (l=llScm, d=CI.Sbm) 0 DS2 (l=llScm, d=0.4pm)

+ q d

.

0.00)

I

/

I

I

,

,

/

,

I

,

0.0000

0.00

0.20

0.40

0.60

0.80

I

0.00

d Cm) Fig. 1. The emittance optimized FS.

/

,

,

,

I

,

I

,

I

,

1.00 0.05

0.10

0.15

0.20

0.25

I (%)

as a function of the probe diameter of each

necessary to take also into consideration that the DS2 system is 2 meters shorter than the DS system. Fig. 2 and Tables 4-9 show that the DS2 system is more promising for using in compact MP with submicron resolutions (d = 0.8 pm and d = 0.4 pm> at 6 2 0.04%.

Fig. 2. The emittance as a function of the momentum spread of the beam of each optimized FS for some probe diameters.

On the other hand, the DSI system exceeds the DS2 system and compares slightly unfavourably with the DS system in E * at 6 5 0.03%, d = 0.8 pm and d = 0.4 km. Hence it follows that the DSI system could be more effective in operation under such conditions.

Table 5 The way of getting necessary MP resolution (d = 0.8 pm) at corresponding values of parameter DS changing the parameters of the object slit and angular collimator is shown

6 and optimal emittance due to the system

DS System (d = 0.8 pm) 6 (%)

rlx (pm)

r, y ( pm)

0 (mrad)

I$ (mrad)

E ( Frn2 mrad’)

0.00 1 0.010 0.040 0.060 0.100 0.150 0.200 0.250

48.1198 42.8193 18.1586 11.5241 10.2245 9.9192 8.4625 6.6291

8.1948 4.0916 2.7352 2.8165 2.8084 1.5059 I .0922 1.1377

0.0244 0.0356 0.0280 0.0216 0.01 I I 0.0058 0.0041 0.0036

0.0147 0.0107 0.0050 0.0030

2.26E I .07E l.lOE3.34E 6.48E 1.68E 5.89E 2.8OE

0.00I3 0.00 I2 0.00 IO 0.0006

Table 6 The way of getting necessary MP resolution (d = 0.4 pm) at corresponding values of parameter DS 1 changing the parameters of the object slit and angular collimator is shown

+ 00 + 00 01 - 02 - 03 - 03 - 04 - 04

6 and optimal emittance due to the system

DS 1 System (d = 0.4 pm) 6 (lo)

rIx (pm)

rl y (pm)

B (mrad)

4 (mrad)

E (hrn’

mrad’)

0.001

12.5759 10.7654 6.53 17 5.1122 5.0829 3.2903 3.5284 2.9346

4.2792 2.4370 I .8365 I .3436 I .2067 0.8597 0.5947 0.6248

0.0176 0.026 1 0.0276 0.0192 0.0078 0.0070 0.0043 0.0373

0.0203 0.0105 0.0040 0.0028 0.0011 O.CQO8 0.0007 0.0005

3.08E 1.15E-01 2.15E 5.98E 8.59E 2.65E I .07E 5.23E -

01

0.010 0.030 0.050 0.100 0.150 0.200 0.250

02 03 04 04 04 05

V. Brwhnik. Table 7 The way of getting necessary DS I changing the oarameters DS

S. Lehed’/Nucl.

131

Instr. and Meth. in Phys. Rex B 122 (1997) 127-132

MP resolution (d = 0.8 pm) at corresponding values of parameter of the object slit and angular collimator is shown

6 and optimal emittance

due to the system

I System (d = 0.8 pm)

( w)

6 (%)

r,, (pm)

rlv

0.001 0.010 0.040 0.060 0.100 0.150 0.200 0.250

24.7477 22.8770 15.8468 12.0497 8.6538 6.6171 6.9661 5.2354

8.1004 4.4349 2.7916 2.3545 2.3259 2.1558 1.3106 0.9953

Table 8 The way of getting necessary DS2 changing the parameters

0 fmrad)

4 (mrad)

E (Frn’

0.0335 0.0226 0.0256 0.0252 0.0189 0.0139 0.0088 0.0083

0.025 1 0.0225 0.0071 0.0049 0.0023 0.00 12 0.0014 0.0012

2.69E 8.26E I .29E 5.598 I .43E 3.86E 1.73E 8.17E

MP resolution (d = 0.4 pm) at corresponding values of parameter of the object slit and angular collimator is shown

-

mrad’) 00 01 01 02 02 03 03 04

6 and optimal emittance

due to the system

DS2 System (d = 0.4 pm) l5 (%)

rt,

0.001 0.01 0.03 0.05 0.08 0.10

4.0337 3.6401 2.3741 I .5995 I.9113 I .6503

(w)

rlv (Pm)

8 (mrad)

4 (mrad)

E (pm’

I .9645 1.7513 I .2975 0.7 152 0.5961 0.6764

0.0912 0.0866 0.0889 0.0738 0.0373 0.0333

0.0064 0.0043 0.0047 0.0066 0.0043 0.0028

7.36E 3.768 2.05E 8.86E 2.90E 1.65E

mrada) -

02 02 02 03 03 03

Table 9 The way of getting necessary

DS2 changing

the parameters

MP resolution (d = 0.8 pm) at corresponding values of parameter of the object slit and angular collimator is shown

S and optimal emittance

due to the system

DS2 System (d = 0.8 pm) s (%o)

rlA (pm)

rlq (I*m)

f3 (mrad)

$J (mrad)

E ( pm2 mrada)

0.001 0.01 0.03 0.05 0.08 0.10 0.15 0.20

8.0577 7.7125 5.6521 2.9523 2.4964 2.5 154 2.2616 2.7077

3.9206 3.477 I 2.7004 I .9876 I .4386 1.1956 0.9065 0.9374

0.1091 0.1837 0.2038 0.2601 0.1054 0.08 1 I 0.0546 0.0355

0.0073 0.0059 0.0070 0.0078 0.0070 0.0063 0.0046 0.0029

4.01E 4.68E 3.48E 1.90E 4.27E 2.47E 8.24E 4.17E

Compare the DS system with the analogous T system [4,5]. The T system and the DS system are similar in the main geometrical parameters (I, L, g, ra). The systems differ only in the arrangement of the lenses and values of their excitations. Owing to these differences the T system is advantageous over the DS system in achieving high probe current (I, 1 100 pA) MP regimes (PIXE, RBS) at submicron resolutions (d = OS- 1 pm>, since the T system in these regimes has a 4-6 times greater value E* [4,5] than the DS system. In Ref. [4] the probe current was

-

01 0I 01 01 02 02 03 03

shown as a function of the probe diameter of each system assuming an ion source/accelerator brightness of 5.3 pA/( pm* mrad* MeV) for a 3 MeV H+ beam provided by the Melbourne Pelletron accelerator. Numerical calculation proves that the DS system could also provide Ip = 100 pA at the mentioned conditions, but at a greater value of resolution (d = 1.6 pm). At the same time the DS system could provide higher resolutions (up to d = 0.025 pm at r, = 0.5 pm) for such MP techniques as STIM, IBIC and SEU, since the DS system has higher

132

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Instr. und Meth. in Phys. Res. B 122 (1997) 127-132

demagnification factors (D,Y = 133.4, DY = - 42.5) than the T system ( D,l-= 3 I .6, D, = - 22.9).

Acknowledgements The authors wish to thank Mr. A.G. Ponomarev assistance in the preparation of this article.

for the

3. Conclusion This work on the basis of numerical studies of short (I < 3.2 m) lens systems consisting of three magnetic quadrupole lenses represents some optimal FS suitable for use in compact nuclear MP in a wide range of parameter 6 (0.001 I 6 I 0.25). It shows that the optimal system DS2 (I = 119 cm) is promising for the use in compact nuclear MP with sabmicron resolutions (d = 0.4 /*.rn and d = 0.8 pm), especially based on an accelerator with 6 2 0.04%. On the other side, the optimal DS 1 system (I = 219 cm) has some advantages at 6 5 0.03%. This work also shows that the shorter optimal systems (DSl and DS2) can successfully compete with the longer optimal system CDS) even at 0.1 pm < d I 0.4 pm and 6 = 0.01%. Systems of DS type and T type [4,5] are complement to each other and can be transformed into one another on the same beam line without large expenses.

References Legge, Nucl. Instr. and Meth. B 3 (1984) 561. Grime, M. Dawson, M. Marsh, I.C. McArtur and F. Watt, Nucl. Instr. and Meth. B 54 (1991) 52. [31 V. Brazhnik, V. Khomenko, S. Lebed’ and A. Ponomarev, in: Proc. 4th Int. Conf. on Nuclear Microprobe Technology and Applications, Shanghai, China, 10-l 4 September 1994. Nucl. Instr. and Meth. B 104 (1995) 69. D. Jamieson, S. Lebed’, G. [41V. Brazhnik, A. Dymnikov, Legge, A. Ponomarev and V. Storizhko, Nucl. Instr. and Meth. B 104 (1995) 92. [51V. Brazhnik, A. Dymnikov, S. Lebed’, A. Ponomarev and V. Storizhko, Sumy, Scientific preprint IAP-09 (1993).

[II G.J.F. 121G.W.