On the calibration of low-energy ion accelerators

281

Nuclear Instruments and Methods in Physics Research B45 (1990) 281-284 North-Holland

ON THE CALIBRATION W.N. LENNARD, Department

OF LOW-ENERGY

S.Y. TONG,

of Physics and Interface

ION ACCELERATORS

G.R. MASSOUMI

Science Western,

and L. WONG

The University of Western Ontario, London,

Ontario N6A 3K7, Canada

The pulse height measured in a silicon detector for MeV 4He ions backscattered from a monoisotopic target, e.g. Au, has been compared to that from a radioactive 241Am source. Using previous results for the so-called “pulse height defect”, including the effects of nonlinear detector response, we have determined the incident beam energy at. - 2.4 MeV with a precision of - 3 keV. The data are in good agreement with a calibration performed using the 27Al(p, Y)~*S~ nuclear reaction resonance technique.

1. Introduction The usually row, [l].

energy

calibration

performed

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using

of

particle

nuclear

resonances

with

27Al(p, v)*~S~ reaction

accelerators

reactions large has

having cross

been

is nar-

sections

used

most

width is - 80 eV, and the location of the resonance at 991.90 + 0.04 keV is ideally suited for those machines that are routinely used for Rutherford backscattering studies (RBS). Additionally, for single-ended accelerators, the same resonance can be exploited using the molecular beam, Hl. Care must be taken in this latter case to relate the y-ray yield correctly to the projectile energy for either thin or thick targets [2-41. There is a broadening of the step in the y-ray count rate increase at resonance, due to the center-of-mass kinetic energy imparted to the two protons by their mutual Coulomb repulsion on breakup at the target surface. In addition to the (p, y) method, there also exist sharp (p, n) threshold reactions suitable for energy calibration purposes. Various investigators have used the precise measurement of y-ray energies in high resolution Ge detectors arising from direct capture reactions to measure the beam energy [5]; here, attention must be paid to Doppler shift considerations. Time-of-flight measurements have also been used [6] for calibration purposes. The use of RBS measurements to determine an internal energy calibration offers several advantages, the most obvious being that it is not restricted to discrete resonance energies but can be used continuously in conjunction with a radioactive alpha source, e.g. 241Am. Conversely, there are inherent disadvantages in the use of charged particle detectors as the principal energy sensing element of a calibration scheme: (1) the thickness of the surface dead layer must be known or measured, and (2) the energy lost in the sensitive volume of the detector via non-ionizing events (i.e. arising from so-called nuclear energy loss) must be known. The frequently,

since

0168-583X/90/$03.50 (North-Holland)

the resonance

0 Elsevier Science Publishers B.V.

contributions of these two effects become less significant, however, for energies in the region 2-5 MeV. Variations of this technique have been attempted in earlier reports. Garnir et al. [7], Langley [8], Mitchell et al. [9] and Scott and Paine [lo] have all used the elastic scattering approach to calibrate the accelerator energy scale. The data analysis given in the latter report was in fact incorrect in that no consideration was given to the unique response of Si detectors to charged particles of different atomic number (i.e. protons and alpha particles), a phenomenon that has been recognized for some time [ll]; i.e. pulse heights of elastically scattered protons were compared to those of alpha particle products from the 15N(p, a)“C nuclear reaction, without regard to differences in both the window losses and non-ionizing contributions. In any case, new results concerning the response of Si charged-particle detectors [12] suggests that their use in accelerator energy calibration should be reviewed at this time, notwithstanding these earlier experiments.

2. Experiment The objective of the experiment was to determine the beam energy as accurately as possible near 2.4 MeV, where there is a dearth of suitable nuclear resonance calibration energies. In fact, the measurements described here can be applied with equal success in the 2-5 MeV energy region. The experimental arrangement was that typically used in RBS measurements. A beam of 4He+ ions was accelerated using a 2.5 MV Van de Graaff accelerator, magnetically analyzed and collimated by a series of defining slits. We set the differential voltmeter to read DVM = 2400 for the measurement. The resultant beam spot at the target position had a diameter of - 0.5 mm and an angular divergence of 0.05 O. A pure gold polycrystalline target was mounted on the target holder for the backscattering measureIII. EQUIPMENT

282

W.N. Lennard et al. / Calibration of low-energy ion accelerators

ments. A 241Am standard source was positioned slightly below the scattering plane to provide simultaneously the absolute energy calibration for the solid state detector. The Si surface barrier detector, located at a scattering angle of 150 o (& 0.5 o ) with respect to the incident ion beam, was collimated to use only the central area to reduce edge effects. Its depletion depth was 100 urn, and the nominal Au layer was 40 ug/cm’. The detector signals were processed using a charge-sensitive preamplifier and a linear amplifier whose output was sent to an ADC using 4096 channels. A high-precision pulse generator whose integral linearity had been previously established was operated simultaneously for all measurements, and all measured pulse heights were referenced to pulser values to circumvent problems arising from ADC nonlinearities. The strict linear relationship between pulser values and measured pulse heights had been confirmed in earlier measurements using y-ray sources and a Ge detector [12]. We measured both the effective source thickness and the thickness of the detector dead layer independently by the usual source or detector rotation method [9,11,12]. The accelerator was calibrated via the 27A1@, y)28Si nuclear resonance at Ep = 991.90 keV, using both monatomic (H+) and molecular hydrogen (Hi) beams. A generating voltmeter mounted within the pressure vessel provided a convenient secondary standard for the accelerator. Its output was monitored by a precision differential voltmeter (DVM) with a sensitivity of 10p4. The DVM readings corresponding to the resonance energy could be determined with a precision - 0.5 kV. For the molecular ion case, we took the half-height position of the DVM to correspond to 1982.8 kV considering the molecular shift [2-41, with an assumed uncertainty of 1 kV. The DVM was known to have a linear response within 0.05%, with regard to interpolation or extrapolation to other energies.

3. Results and discussion From an extrapolation of the (p, y) calibration, we determined that the DVM = 2400 setting corresponded to a true beam energy of 2410.3 f 1.5 keV. Fig. 1 shows the data obtained for the detector window thickness measurement using 241Am alpha particles. We found that the energy loss for normally incident alphas at 5485.6 keV was AE, = 12.5 f 1.0 keV, yielding an effective thickness (assuming that the window material is pure Au) of 56.5 f 4.5 pg/cm2. This result has been discussed in some detail in ref. [12] and is consistent with other investigations [8,9] that found the effective thickness to exceed that specified by the manufacturer. The measured effective thickness of the source was AE, = 2 + 0.5 keV.

5790

g

5785

Gi I w

5780

Y 2

5775

5770

-60

-40

-20

DETECTOR

40

;LT

60

(cd:;.)

Fig. 1. Pulse height data as a function of detector tilt angle to find the effective window thickness of the Si detector for 241Am alpha particles. The smooth curve is a fit: PH = A, - A,sec 8. The thickness can be determined from the value of A,. The ordinate gives values relative to a pulser reference.

Energy deposited in atomic motion, AE,,, is not available for creating electron-hole pairs. AE,, was calculated by standard procedures [13], including the effect of electronic stopping for the recoil Si ions. Values for AE, as a function of incident projectile energy are shown in table 1 for both ‘H and 4He ions. We have found that the values for the non-ionizing loss (in keV) are well described by a function of the form: AE,=y[e”“2.47-l]*,

(1)

where r is the particle energy in MeV, y = 3.2850 (11.151) for ‘H (4He) ions, and (Y= 0.2062 (0.10) for ‘H ( 4He) ions. Thus, the energy that is actually deposited in the active detector volume for normally incident charged particles is: Ed = E, - AE, - AEw - AE,. For the alpha-emitting source ( 241Am), we find Ed = 5457.3 f 1.12 keV, with AE, = 2 keV, AE, = 12.5 keV, and AE, = 13.8 keV. The uncertainty is derived from: (1) SE, = 1.0 keV for the window thickness;

Table 1 Values (in keV) for the non-ionizing energy loss, AE,, of ‘H

and 4He ions in silicon as a function of incident energy AE,(‘H)

AEJ4He)

500

2.4

1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

2.7 3.1 3.4 3.6 3.9 4.2 4.4 4.7 4.9 5.1 5.4

9.5 10.3 10.9 11.3 11.8 12.1 12.5 12.9 13.2 13.5 13.8 14.1

Energy [keV]

W.N. L.ennardet al. / Calibration of low-energy ion acce2erator.v 1000

100

The response of Si charged-particle detectors has recently been shown to be slightly nonlinear even for ions of the same atomic number [12]. This nonlinearity can be described empirically by noting that the pulse height at room temperature, PH, is given by

“II;Ij

10 -0

u ‘y

1 1500 1000 -

P 4

3

100 -

1

Pu

PH=e,

2000

P 239

241

Am

‘““Cm

10 -

Channel

number

!1

Fig. 2. Pulse height spectrum measured for 4He ions scattered to 150 o from a thick Au target; the incident energy is EiEinc = 2.4 MeV. The upper panel shows the region corresponding to the elastically scattered ions. The lower panel shows the peaks from the alpha emitters, indicated by the respective isotope. ‘Ihe peaks labelled Pi (i = l-4) produced by the reference pulser are used to determine the pulse height at the gold edge relative to that from 241Amby interpolation or extrapolation.

SE, = 0.5 keV for the source thickness; SE, is not considered at this time, as its value represents a systematic uncertainty; this point will be addressed when comparing the RBS and 24?4m pulse. heights. Fig. 2 shows the backscattering spectrum measured for 4Hef particles incident at the setting DVM = 2400 for the accelerator. We also show the 241Am 01spectrum at the upper region of the ADC with the purser peaks also present. The radioactive source used contained three alpha emitters - 23gPu 241Am and 244Cm - all of which can be seen in the figke. The count rate was kept purposefully small for these measurements to avoid gain shifts due to rate. All pulse height values were determined relative to those of the pulser in any case. Using the Au edge, we measured the pulse height ratio, PH,/PH, = 0.4061 f 0.0003, where the largest uncertainty arises from the determination of the half-height channel in the RBS spectrum. PH,, was determined from the most probable value. For the known geometry, this pulse height corresponds to a fractional retained energy of K, = 0.92695 rL:0.00016 for the backscattered projectiles, where the uncertainty derives from the uncertainty (&OS “) in the laboratory scattering angle. Thus, the energy deposited in the Si detector, Ed, is given by Ed = K,E, - AEw - AE,, = KbEhc - 29.6 (& 1.5) keV, where Einc is the incident beam energy. The uncertainty has been derived in the same marmer as for the 241Am case, with SE, = 1.5 keV at this lower energy. (2) (3)

283

E,-AE,

f a.%

dE Eg- kS( E) ’

where ee = 3.67 eV per electron-hoIe pair, E, is the kinetic energy of the particles incident on the detector, AE;, is the non-ionizing energy loss in the sensitive volume, AEw is the energy lost in the detector dead layer, S(E) is the stopping power of the incident ion in Si [S(E) > 0] taken from ref. [14], and k is a constant independent of the atomic number of the charged particle, k = 2 x low4 (units of ~/el~tron-hole pair). We have calculated the pulse height corresponding to the 241Am alphas, including the dead layer and window losses, and find PH,, = 5523.3 + 1.1 keV, using eq. (1). Thus, PH,, = 2243.0 + 1.7 keV. We then used eq. (1) iteratively to find the value of Einc which satisfies dE EU e” E, q,-kS(E)

I

= 2243.0,

(3)

where E, = K,Ei, - 18.1( AE,) and El = 11..5( AE,& in keV. We thus obtain E, = 2413.8 + 2.5 keV, in close agreement with the energy 2410.3 rt: 1.5 keV determined from the (p, v) calibration. If we consider the values given in table 1 for the non-ionizing contribution arising in the Si detector, and allow a 20% systematic uncertainty, then our overall uncertainty in the beam energy increases to 2.8 keV. If we had not used the semiempi&al results describing the detector nonlinearity [12], and instead assumed a linear response, we would have arrived at the conclusion that the incident beam energy was 2422.8 keV - in major disagreement with the (p, y) results. For increasing accelerator energies, the absolute uncertainty in a calibration performed in this manner can be reduced to - 2 keV as both the non-ionizing and window losses for the backscattered 4He ions and the 241Am alpha particles become more equal. Given the scarcity of appropriate nuclear resonances at higher beam energies, the RBS technique thus becomes competitive with conventional calibration procedures.

4. Conclusions A satisfactory technique for determining the energy calibration of an ion accelerator in the energy region 2-5 MeV has been demonstrated. In fact, the method becomes more reliable for incident 4He ion energies higher than that studied here. This approach has the advantage that it can be applied continuously at any beam energy, without the need for interpolation beIII. EQ~PMENT

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W.N. Lennard et al. / Calibration of low-energy ion accelerators

tween nuclear resonance energies as for (p, y) or (p, n) calibrations. A disadvantage in the technique is the necessity of determining the effective dead layer for the particle detector. This technique should be of most benefit to researchers engaged in ion beam studies where the experimental setup already exists. It should not be seen as a substitute for nuclear reaction techniques, as its intrinsic precision is more limited due to uncertainties in some of the parameters affecting the data analysis. We suggest that the good agreement between the RBS and the (p, y) calibration data provides further evidence supporting the nonlinear behaviour of Si charged particle detectors. The authors gratefully acknowledge the technical assistance of H.M. Adams and Z. Margaliot during the course of this work.

References [l] J.B. Marion

and F.C. Young, Nuclear Reaction Analysis (North-Holland, Amsterdam, 1967) p. 145. [2] P.F. Dahl, D.G. Costello and W.L. Walters, Nucl. Phys. 21 (1960) 106.

[3] W.L. Walters, D.G. Costello, J.G. Skofronick, D.W. Palmer, W.E. Kane and R.G. Herb, Phys. Rev. 125 (1962) 2012. [4] J.W. Butler and C.M. Davisson, Nucl. Instr. and Meth. 149 (1978) 183. [5] C. Rolfs, W.S. Rodney, S. Durrance and H. Winkler, Nucl. Phys. A240 (1977) 221. [6] H.-B. Mak, H.B. Jensen and C.A. Barnes, Nucl. Instr. and Meth. 109 (1973) 529. [7] H.P. Garnir, G. Weber and L. Winand, Nucl. Instr. and Meth. 111 (1973) 549. [S] R.A. Langley, Nucl. Instr. and Meth. 113 (1973) 109. [9] J.B. Mitchell, S. Agami and J.A. Davies, Radiat. Eff. 28 (1976) 133. [lo] D.M. Scott and B.M. Paine, Nucl. Instr. and Meth. 218 (1983) 154. [ll] G.F. Knoll, Radiation Detection and Measurement (Wiley, New York, 1979) p. 395. [12] W.N. Lennard, H. Geissel, K.B. Winterbon, D. Phillips, T.K. Alexander and J.S. Forster, Nucl. Instr. and Meth. A248 (1986) 454. [13] K.B. Winterbon, Ion Implantation Range and Energy Deposition Distributions, Vol. 2 (Plenum, New York, 1975) and AECL Report no. AECL-5536 (1976). [14] J.F. Ziegler, He: Stopping Powers and Ranges in All Elements (Pergamon, New York, 1977).