Nuclear Instruments and Methods in Physics Research B9 (1985) 259-262

North-Holland, Amsterdam

259

STOPPING CROSS SECTIONS OF He+ IONS IN BISMUTH

KULDEEP and Animesh K. JAIN

Nuclear Ph_wcs Diuision, Bhabha Atomic Research Centre, Bombay 400 085, India

Received 22 October 1984 and in revised form 5 March 1985

The stopping cross sections, c(E), of He+ ions in bismuth have been measured by Rutherford backscattering spectrometry (RBS)

at incident energies ranging from E = 1.6-3.4 MeV. The energy loss of He + ions and thicknesses of the bismuth films deposited on aluminium substrates were determined from the RBS spectra at each energy for scattering angles of 130” and 165”. The film

thicknesses of some of the samples were also measured by weighing, and the results compared with those from RBS. Parameters for

energy dependence of stopping cross section in the Varelas-Biersack interpolation formula have been obtained for bismuth from a fit

to all the available experimental data. Accuracy of our method based on RBS is demonstrated by measurements on copper, for which

c(E) is already well studied. It is also shown that reliable c(E) values may be obtained even on samples with non-uniform film

thickness.

1. Introduction

He+ ions in the energy range of 1-3 MeV are commonly employed as probes for depth profiling by

Rutherford backscattering spectrometry (RBS). To ob- tain the conversion from backscattered energy to depth, it is necessary to accurately know the stopping cross \ections of probing He+ ions in the target material. An extensive study on this subject has been carried out by various workers, and consolidated data for some fifty \even elements have been tabulated by Ziegler [l]. The measurements of stopping powers of He+ ions in bi- bmuth in the energy range of 20 to 300 keV, and 400 keV to 1.9 MeV have been reported by Eckardt [2] and Borders [3] respectively. In this paper, we present our measurement of He+ stopping powers in Bi over the energy range of 1.6 to 3.4 MeV. Our measurements thus supplement the data of Borders [3].

2. Experimental

Polycrystalline aluminium samples were electro- polished in an electrolyte containing 90% methanol and 10% perchloric acid to produce a mirror finish. Bismuth films of thickness ranging from 2500 to 7000 A were deposited on these polished aluminium substrates by vacuum evaporation. The film thicknesses were accu- rately determined by RBS, as described in sect. 3. Some of the substrates were weighed on a microbalance prior to deposition of the films. The film thicknesses on these samples were obtained from a second weighing after deposition. The microbalance had an accuracy of k 10 pgm. The error in measurement of “average” film thick-

0168-583X/85/%03.30 Q Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

ness by weighing is estimated to be I< +5%. The agree- ment between average thicknesses obtained by RBS and by weighing was well within this limit of error.

The RBS measurements were carried out using a well collimated 1 mm diameter He+ beam from a 5.5 MeV Van de Graaff accelerator. The beam was incident normal to the sample. The backscattered ions were detected at scattering angles of 165” and 130” using surface barrier detectors and the usual electronics. The incident beam energies were determined by measure- ment of the analysing magnetic field with an NMR gaussmeter, calibrated using ‘Li(p, n)‘Be reaction. The RBS spectra were collected for incident energies of 1.6 MeV to 3.4 MeV, in steps of 200 keV. The analysed

spot on the target was frequently changed to avoid build up of carbon layer. The stopping cross section z(E) was obtained from the observed widths of Bi peaks using a procedure described in sect. 3.

In order to cross-check the accuracy of the method used, we have also measured the stopping cross sections of He+ ions in copper, which are already well studied [l]. Our results on copper (presented in sect. 4) are in good agreement with the tabulated values of Ziegler [l]. Further, measurements at five different points on a bismuth sample were made at 2.0 MeV energy to dem- onstrate the insensitivity of our measurements towards variations in film thickness across the sample.

3. Calculational procedure

In this section, we shall describe the method used by us to determine the film thickness (Nt), and the stop- ping cross section C(E) from the observed RBS spectra.

260 Kuldeep, A. K. Jain / Stopping cross sections of He + in Bi

3. I. Determination of (Nt)

The total number of counts, A, under the peak of the film material is given by

A = (n;t)Qao,(E,), (1)

where Q is the number of incident ions, St is the solid angle subtended by the detector, (Nt) is the number of atoms per unit area in the film, and Us is the scattering cross section of the film atoms for incident He ‘- ions of energy E,. Since a reliable measurement of Qf;2 is difficult, we have made use of the observed Al heights to obtain QU, as is customary in most RBS analyses. the observed height of the Al substrate edge can be expressed by,

H*I=(fAi(E1)(SE)(Q~t)/ft(El)l~: (2)

Here uA, (E,) is the scattering cross section for AI at E,,

which is the energy of He+ ions immediately before scattering at the film/substrate interface, and SE is the energy width of a channel. The stopping cross-section factor, [c(E)]: used in eq. (2) is defined by

[~(E)]%=K,c~(E)+ /set Blt-Y(K,E) (3)

where K is the kinematic factor and 0 IS me laboratory scattering angle. The subscript x and the superscript y denote the scattering atom species and the stopping medium respectively. eA1( E) is well studied experimen- tally and is tabulated in ref. [l]. The energy E, was estimated by

E, =EO--txAE,,,, (4)

where AE,, is the observed energy shift of the Al edge with respect to the surface energy KAIEO. The fraction of energy loss in the inward path, (Y, is given to a good

approximation by

~=c:‘(E,)/{c’(E,)+~‘(K,,E,)IsecBI}. (5)

Since e f( E) for the film is unknown in principle, a! was calculated using the tabulated values of e’(E) from ref. [If. Since the energy loss in the film is small, and n: in eq. (4) involves only ratios of stopping cross sections, this approximation does not seriously affect the value of E,. The area1 density Nr of the film can be determined

by comparison of eqs. (1) and (2), which gives,

[ 1 2

(iw}=$; 3 6E A,.

[C(EI)lAI Here it is assumed that the scattering cross section is directly proportional to (Ztarget/E)2. In eq. (1) for the area of the film peak, we have not accounted for the energy dependence of the scattering cross section, ut. The corrected value of Nt was obtained by following ref. 141 and is given by,

(NE) = (Nt)& - (eW)(W&%Jj

= tNt),(E,/&), (7)

where (Nt), is the uncorrected area1 density given by

eq. (6).

The stopping cross section factor for the film is related to the width of the film peak, AE. by

[+%)];=W’(W (8)

The stopping cross section factor [ r(E,)j f was de- termined at each energy and angle from the energy widths of the film peaks and the calculated values of

(Nt). The measured [c(&)]: values were also con- sistent with the observed film to Al signal height ratios. The ratio of [r( E,)] i for scattering angles of 130” and 165’ at a given energy was found to be - 1.27 as expected from geometrical considerations.

The stopping cross section, e(E), is obtained from

the measured [e-f&,)]: values from the following set of relations based on ref. [5]

(9) E=[K,&,+ lsec eI&,,,]/[K,+ /set @I], P)

E,, = ( 4, + 4 ),‘2, (11)

E,“, = [ K,E, +(K,E, - AE)]/2 = K,& - (AE)/2.

02)

The quantity E, in eq. (11) is defined already by eqs. (4) and (5). Since E is less than E,, our measurements at E0 ranging from 1.6-3.4 MeV yield ef E) values for the energy region 1.3-3.2 MeV in bismuth. It may be noted here that effect of stopping power variation with energy

over the entire path of the He+ ions is taken care of by eqs. (9)-(12) up to the second order in energy [5].

4. Results and discussion

The stopping cross sections of He+ ions in Bi have been determined at incident energies from 1.6 to 3.4 MeV using the method described in sect. 3. The t values at each energy were evaluated for all the samples of different thicknesses. In fig. 1, we have plotted the measured E values (filled circles) from different samples along with the experimental results of Eckardt (squares) and those of Borders (open circles). In the energy range of 1.6-1.9 MeV where our measurements overlap with those of Borders [3], about 60% of our points are in good agreement with the earlier measurement (see fig. 1). However, an average of all the points suggests a trend towards higher c(E) values than those of Borders. Since our measurements alone do not define the corn-

plete shape of the stopping curve, we have included all the available experiments results on bismuth [2,3] in a fit to obtain parameters of the Varelas-Biersack inter-

0 ECKAROT (19781

0 BDRDERS (19741

. PRESENT WORK

Fig. 1. The stopping cross sections of He+ ions in bismuth as a

function of energy. The continuous curve is the best fit [eqs. (In)-(15)] to al1 the available data shown in the figure. The

dashed curve shows the best fit excluding the data of Borders [eqs. (16)-(17)j.

polation formula [l&j. The expression for c(E) ob- tained in the energy range of 20 keV to 4.0 MeV is shown in fig. 1 by a continuous curve and is given by,

(l/c) = (1/Q,,) +W~HrCH) f13)

where,

e Low = s .473 z?s*72, (14)

cHIGgl = (125 200/E) ln[l +(350.3/E)

+ 7.401 x 10-Q] (151

and E is the energy in keV. Since there are no measure- ments available other than those of Borders in the region of peak in the stopping curve, this fit is some-

what constrained to pass close to these points. This fit starts deviating from measurements of Eckardt [2] be- yond 200 keV (see fig. l), and our measurements also show a trend towards higher stopping values between 1.5 and 2.0 MeV. In view of these, another fit was attempted by inclu~ng only measurements of Eckardt 121, and the present work. The result of this fit is shown as a dashed curve in fig. 1 and is given by eq. (13) where,

cLow = 5.581 E".5794, (16)

~HIGH=(~O~~~/~) ln[l+(4376/E)

+ 1.197 x lO_ZEj (17)

This fit (dashed line in fig. 1) passes nicely through all the points of Eckardt, but predicts higher stopping

power near the peak by about 7%, as compared to the previous fit (solid line in fig. I). This discrepancy is slightly more than the estimated error of i_S% in the work of Borders [3]. It would be interestlng to extend our measurements in the region of the peak. Unfor- tunately this could not be done with our accelerator which has stable operation only above 1.5 MeV.

The observed scatter in data points in fig. 1 at a particular energy is mainly due to variations seen from sample to sample. The exact reason for this variation of c from one sample to another is not clear. The depen- dence of e on film structure [7,8], or inco~oration of different amounts of impurities in the samples, prepared under slightly different conditions could be possible causes for this scatter. Such a scatter in data points from independent measurements is however not uncom- mon in this energy range and has been seen pro~nent~y in Si, Ti, Ge. Pt, and Au [l] by earlier investigators.

In order to check the accuracy of our method, we have made measurements of stopping cross sections in copper, which is already well studied. The results at four different energies are presented in fig. 2 as open circles. The solid line in fig. 2 represents the tabulated values of

6 in copper taken from ref. [l]. The error bars on the points denote a variation in e of 15%. In comparison with the tabulated values of Ziegler [l], our results on Cu are in agreement within 3% or better. Based on the experimental uncertainties and errors in e values of Al which is used to calculate (Nf) of film, we estimate our method to be accurate within f 5%. Further, our method is insensitive to variations in film thickness across a sample. This is demonstrated in fig. 3, where filled and open circles represent the e values obtained by BBS

; 60 al

Y

0 5 50

: 0 G

40 1.0 2.0 3.0 4.0

ENERGY (Met/)

Fig. 2. The measured stopping cross sections (0) in copper as a function of energy. The continuous curve shows the tabulated

values of c from ref. [l], The error bars denote a variation of

+ 5%.

Kuldeep, A.K. Jain / Stopping cross sectlons of He’ in Bi

0 RBS

0 WEIGHING

5 130’

g

I

0

2 125 0 ul

120 O1 I I I 1 1 -15 -10 -5 0 5 10 15

DISTANCE FROM CENTRE (mm)

Fig. 3. The stopping cross sections for 2.0 MeV He+ ions in

bismuth measured at different positions on the same sample by weighing (0). and by RBS (0) methods. The dashed line shows the average of RBS measurements.

and weighing methods respectively at different points on the same sample. The width, A E, of the film peak in the RBS spectra taken at points from one end of the sample to the other showed a gradual increase (upto 15%) indicating continuous variation of film thickness across the sample. Since one gets only an average value of (Nt) by weighing, the corresponding [cl, and hence the stopping cross section values (open circles in fig. 3) naturally show a similar variation. On the other hand, the (Nt) values obtained from RBS follow the same variation as A E such that their ratio, ft], remains fairly constant. Thus the stopping cross sections obtained by our method described in sect. 3 are insensitive to thick- ness variations as can be seen from the filled circles in fig. 3. The advantage of the RBS method is thus clearly

brought out.

5. Conclusions

We have measured the He+ stopping cross sections in bismuth in the energy range of 1.3-3.2 MeV. Our measurements extend the range of earlier data from works of Eckardt [2] and Borders [3]. Our method is based on analysis of RBS spectra alone and does not

require independent and precise knowledge of film thickness. The method can be used with any suitable substrate for which the stopping cross sections are well established. Substrates such as Al, Cu, and Si, for example, could be used [9]. The accuracy of the method has been demonstrated by comparison of our measure- ments on copper with the established values. Our mea- surements were also shown to be insensitive to film thickness non-uniformities across a sample. Our results are in reasonable agreement with the trend of earlier measurements in bismuth.

We thank the operation staff of the Van de Graaff Laboratory, BARC, for skillful operation of the acceler- ator. We thank M.J. Kansara and V.P. Salvi for assis- tance in RBS work.

References

[l] J.F. Ziegler, The Stopping and Ranges of Ions in Matter, vol. 4 (Pergamon Press, New York, 1977).

121 J.C. Eckardt, Phys. Rev. A18 (1978) 426.

[3] J.A. Borders, Radiat. Effects 21 (1974) 165.

[4] W.K. Chu, J.W. Mayer, and M-A. Nicolet, Ba~kscattering

Spectrometry (Academic Press, New York, 1978) p. 93.

[SJ See ref. 141, p. 277.

[6] C. Varelas and J.P. Biersack, Nucl. Instr. and Meth. 79

(1970) 213.

[7] S. Matteson, E.K.L. Chau, and D. Powers, Phys. Rev. Al4

(1976) 169.

[8] J.F. Ziegler and M.H. Brodsky, J. Appl. Phys. 44 (1973)

188.

[9] J.F. Ziegler and W.K. Chu, Atomic Data and Nuclear Data

Tables 13 (1974) 463.