Nuclear Instruments and Methods in Physics Research A310 (1991) 657-664 North-Holland
& ME'IIlIOaS IN IltlYIICl
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Response functions of Si detectors to monoenergetic electrons and positrons in the energy range 0.8-3.5 MeV * Th. Frommhold, W. Arnold, H. Friedrichs, R. Giibel, R.D. Heil, U. Kneissl, U. Seemann and F. Steiper lnstitut fiir Kernphysik, Unirersitiit Giessen, D-6300 Giessen, Germany
C. Kozhuharov Gesellschaft fiir Schwenonenforschung Darmstadt, D-6100 Darmstadt, Germany Received 25 March 1991 and in revised form 4 July 1991
Dedicated to Prof. Paul Kienle on the occasion of his 60th birthday The response functions of Si surface barrier detectors (depletion depth: 2 ram, active area: 200 ram") to monoenergetic electrons and positrons have been measured in the energy range 0.8-3.5 MeV at the Giessen electron linear accelerator. Lower peak-to-total ratios were observed in the positron response functions compared to electrons. The measured response functions were compared with Monte Carlo simulations enabling a separation of the individual contributions to the response function such as: total energy loss, backscattering, transmission, bremsstrahlung emission. A parametrization of the response function for electrons is given, which allows a reliable approximation of the response function in the investigated energy range.
1. Introduction and motivation An ideal detector should transform the energy spectrum of a radiation source into a pulse height spectrum which is exactly proportional to the incident energy spectrum. T h e deviations from the proportionality, which cannot be avoided when using a real detector, can be described by the response function. The pulse height distribution H(h) produced by a certain detector is related to the incident energy distribution S(Eo) by the following integral relation [1]
H(h) = Jo S( Eo)R ( Eo, h) d E o.
(1 )
Here R(Eo, h) represents the response function of the detector. In the case of monoenergetic incident particles S(E o) is given by a delta function, reducing eq. (1) to
H ( h ) = R ( E o, h).
of electrons or positrons the following p~ocesses lead to an incomplete energy, absorption: - backscattering, - transmission (energy loss), and - bremsstrahlung emission. Furthermore, the Compton process of 511 keV annihilation quanta can lead to an additional energy deposition which manifests itself by a shoulder on the upper side of the full energy peak. In fig. 1 the contributions of the various processes to the response function are shown schematically. For the discussion of the
(2)
In the following we restrict ourselves to the application of Si detectors for the detection of electrons and positrons. Completely absorbed particles give rise to a sharp line which is broadened by the detector energy resolution (full energy peak). In the case of detection * Supported by the Deutsche Forschungsgemeinschaft under contract Kn 154-19.
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Fig. 1. Contributions to the response function (schematically).
0168-9002/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved
658
Th. Frommhokl et al. / Response functions of Si detectors handling system selects electrons or positrons and bends the beam by 50 °. A remote controlled slit system in the symmetry plane of the system enables one to choose certain momentum bins down to a relative uncertainty of A p / p = 0.5%. A further 40 ° bending magnet finally directs the beam into the experimental chamber and discards any secondary electrons and photons. A beam profile and position monitor [17] consisting of a rotating plastic scintillator was used for an accurate beam adjustment. Positron beams of some pA can be produced in the energy range 1-10 MeV. The beam current is nearly proportional to the beam energy [16]. By varying the electron beam intensity incident on the converter the beam intensity behind the converter can be adjusted. This is essential for the detector test, in order to avoid pile-up effects.
theoretical descriptions of these electromagnetic phenomena the reader is referred to the literature [1-9]. The precise knowledge of the response funclinn of Si detectors is of crucial importance for the ana!ysis of various experiments, e.g. in 13-spectroscopy re; the determination of the spectral shape or of the endpoint energy to extract Oa-values, which are often the only way to determine nuclear masses far from stability [I0]. The present investigations of the response functions of Si surface barrier detectors for electrons and positrons have been initiated by recent Bhabha- and Moller scattering experiments [II], which have been performed to search for hypothetical resonances in the Bhabha scattering cross section. The enormous amount of such experiments [12] was prompted by the discovery of narrow line structures in positron- and electron-positron coincidence spectra observed in heavy ion collisions near the Coulomb barrier [13-15].
2.2. Detector arrangement and experimental setup The detector setup is shown in fig. 3. An active collimator (plastic scintillator NE102, area 3 0 x 3 0 mm 2, 10 mm thick) with a slit (3 mm wide, 10 mm high) is used to adjust the electron/positron beam and to define the beam spot and position. The scintillation light is transmitted to a photomuitiplier (Valve 56DUVP) outside the vacuum system via a light guide. The Si surface barrier detector to be tested is mounted 10 mm behind the collimator. The Si detector is operated in anticoincidence with the scintillator. In order to avoid the registration of particles backscattered from the Si detector into the collimator a 5 mm
2. Experimental procedure Z !. Electron and positron beams at the Giessen linac The setup and beam line used at the Giessen 65 McV electron linear accelerator for the measurements of the response function is shown schematically in fig. 2 [16]. A pulsed 25 MeV clcctron beam (pulsc width 2 ~s, repetition rate 600 Hz) produces electron-positron pairs in a 2 mm thick, water cooled tungsten target (c+-c - convcrtcr). A subscqucnt achromatic bcam
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Fig. 2. Electron/positron beam facility as installed at the Giessen 65 MeV electron linear accelerator [16].
Th. Frommhold et al. / Resport~efunctions of Si detectors
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Fig. 3. Details of the expedmental arrangement: active collimator with light guide and photomultiplier, test Si detector and additional Si{Li) detector (dimensions given in mm).
thick aluminium shielding was installed between collimator and Si detector. At a distance of 6 mm behind the Si detector an additional Si(Li) detector was mounted to detect particles traversing the test detector. Conventional electronics was used. The two charge-sensitive preamplifiers for the Si and the Si(Li) detectors and the photomultiplier of the plastic collimator each deliver an energy and a timing signal. The three energy signals were fed directly to CAMAC ADCs. The timing signals produced logical NIM signals in CF-discriminators, which allowed to measure two time differences (Si-plastic, Si-Si(Li)) using CAMAC TDCs. All data were registered event-by-event using a PDP11/73 + microcomputer.
3. Results The response functions for Si surface barrier detectors have been measured for electrons and positrons at eight energies in the range 0.8-3.5 MeV. The detectors (ORTEC TA-022-200-2000) each had a thickness of 2000 ~m, and an area of 200 mm 2 [18]. The front side was covered by a 40 la,g / c m 2 gold layer, the back side
65~
by a 40 p.g/cm z aluminium layer. Thcrcfi~rc, the de. tcctors could be used in a transmission arrangement (fig. 3}. The energy calibration was performed using a :"?Bi source of internal conversion electrons. The energy resolution amounted to about 27 kcV fi}r the 975.b keV IC line of -'UTBi. The response functions of the detectors were measured with the condition imposed that there was no coincident signal from the active collimator (anticoinci. dence); this means that the registered particles had to pass the collimator without any scattering. At low incident energies the spectra arc dominated by the full energy peak with only a small tail to lower pulse heights, due to the backscattered particles. For energies higher than ---. ! MeV the ranges of the electrons/ positrons become larger than the detector thickness. Therefore, a broad bump appears corresponding to the partial energy loss of particles traversing the detector, while the full energy peak decreases. Even at the highest energies investigated in the present experiments a small full energy peak remains due to the longer pathlength, caused by large angle and multiple scattering. Some interesting differences in the pulse height spectra for electrons and positrons could be observed (fig. 4). Positrons stopped inside the detector annihilate with an electron and, with a certain probability, the produced 511 keV annihilation photons can undergo Compton scattering before escapi,g the detector. This causes an additional energy deposition (up to 340 keV) in the detector (see fig. 1}. Therefore, the response functions for positrons exhibit a shoulder at the high energy side of the full energy peak. This coincidence effect obviously reduces the intensity of the full energy peak. In figs. 5a and 5b the peak to total ratios observed in the response functions for electrons and positrons are plotted as a function of the bombarding energy. In the positron spectra, besides the shoulder above the full energy peak (produced by annihilation inside the detector), a further Compton distribution of 511 keV quanta is present at low pulse heights, which were produced by the annihilation of positrons hitting the surrounding material. Therefore, a cut-off energy of 370 keV was used to calculate the total rate. The ratio substantially decreases for both electrons and positrons as a function of the energy (from about 90% at 0.8 lv,~ v tO s o m e n , o/_ .. 3 . 5 ~ , x 1 ~ r:.....~.. . . . . ;... ,k~, whole energy range investigated here, we measured reduced peak to total ratios for positrons compared to the electron data. The difference is mainly caused b.v the summing of the energy loss signal and the signal from Compton scattering of 511 keV annihilation quanta, which, as outlined above, reduces the full energy peak in the case of positrons, and less so by different energy losses and different Mott scattering cross sections of electrons and positrons.
Th. FrommhoM et aL / Response fimctions of Si detectors
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Fig. 4. Measured response functions for'electrons and positrons.
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Fig. 5. Peak to total ratios for electrons and positrons as a function of the energy ( E c u T = 0.37 MeV, (a) linear scale, (b) logarithmic scale).
Tit. FrommhoM et aL / Response functions of Si detectors 4. C o m p a r i s o n w i t h M o n t e C a r l o s i m u l a t i o n s
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4. I. The Monte Carlo program
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The Monte Carlo program developed by Lchmann et ai. at the Stuttgart University [19] was extended and modified for the present problem. The "history" of electrons and positrons traversing a layer of material is simulated, taking into account the following interactions: - scattering off the nucleus (Mott-Born formula), - energy loss by excitation and ionization (including energy straggling), and - energy loss by bremsstrahlung emission. Details of the physical inputs and computational techniques can be found elsewhere [19-22]. Spectra for bombarding energies 0.8, 1.0, 1.25, 1.9, 2.3, 2.8, and 3.5 MeV and additionally some spectra with the exact experimental energies have been simulated (each with 6000-8000 events). The genera.'.cd spectra then were folded with a Gaussian distribution with a half width corresponding to the detector resolu-
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Energy [MeV] Fig. 7. Comparison of simulated peak to total ratios for electrons (full line} and positrons (full squares}.
tion. The resolution was assumed to be independent of energy as was observed in the experiment. This indicates that the resolution is mainly determined by random noise than by statistical noise, because the former are related to the electronic characteristics and the latter depend on the fluctuations in the number of charge carriers produced by the deposited energy.
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Fig. 6. Comparison of the measured response functions for electrons and positrons with Monte Carlo simulations.
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Th. Frommholdet aL / Response[unctions of Si detectors
662
4,2, Results of the simulation and comparison with experiment
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Figs. 6a and 6b show the comparison of the simulated response function for electrons and positrons with the experimental data, The agreement is rather perfect at low bombarding energy, For positrons the Compton scattering of the annihilation radiation had not been calculated in the program, therefore, the Compton distribution above the full energy peak is not reproduced, At the highest investigated energy ( = 3.5 MeV) there seems to bc a worse description of the data in the region of about twice the energy of the huge energy loss bump, However, this might be duc to experimental shortcomings (slight pile-up of energy loss events on the order of one percent). The relative contributions of the different processes to the response function arc summarized in table 1. In fig. 7 the results for the simulated peak to total ratios are shown. The overall agreement is satisfying. There are only small differences between electron and positron spectra, This seems to be reasonable since for positrons all events of total energy loss (full energy peak + Compton distribution) are considered. For a more detailed discussion in fig. 8 the relative deviation
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M MC / Nr M C
M Exp / M Exp
• ' p e a k / " "total - - • " p e a k / • "total E X p / , ~ r Exp e a k / z Vtotal
between experimental results (Exp) and simulations (MC) are plotted. While the experimental data are quite well reproduced for electrons, for positrons the contribution to the full energy peak is overestimated. This might be due to the straggling distribution of positrons, which is narrower than the Landau distribu-
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[MeV]
Fig. 8. Relative deviations RD of experimental peak to total data from the predictions of the simulations.
tion used in the simulation. Furthermore, the Mott cross section for positrons is slightly more forward peaked, leading to a higher penetration depth [6]. These effects have to be included in more sophisticated simulations.
$. Parametrization of the response function A parametrization was developed for an approximatire description of the response function. If the incident energy E 0, the total sum of the spectrum s, the channel width dQ, the detector thickness d, and the energy resolution FWHM are known, the response function R can be calculated for detector thicknesses near 2000 ~m. It consists of four parts:
R=G+T+B+L,
(3)
where G and T represent the full energy peak with bremsstrahlung tail, B the backscattering part and L
Table I Relative contributions of the escape processes and the full energy peak to the response function resulting from the simulations. The full energy peak value includes the Compton distribution in the case of positrons. The statistical errors of the contributions C are given by tr = ~C/8000 for incident energies up to 1.25 MeV and by tr = x/C/6000 for all others. Energy [MeV] 0.80 1.00 1.25 1.50 1.90 2.30 2.80 3.50
Backscattering
Transmission
Bremsstrahlung
Full energy peak
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O.l 18 O.I 12 0.099 0.097 0.077 0.067 0.048 0.028
O.120 O.I I I O.lOl 0.094 0.075 0.069 0.049 0.027
0 0.003 O.113 0.320 0.614 0.783 0.892 0.951
0 0.006 0.I 12 0.335 0.623 0.790 0.892 0.954
0.041 0.057 0.076 0.087 0.057 0.038 0.020 0.007
0.036 0.050 0.074 0.075 0.057 0.037 0.020 0.006
0.841 0.828 0.712 0.496 0.252 O.112 0.040 0.014
0.844 0.833 0.713 0.496 0.245 0.104 0.039 0.013
Th. Frommholdet al. / Responsefunctionsof Si detectors the energy loss peak (fig. 1). G is chosen as a Gaussian function. The bremsstrahlung tail T is approximated by
an exponential function multiplied by a factor - O , that forces the function to approach zero for Q = E o. As approximation for the backscattering part ' 2 Q/Eo_ 1 )2 + c produces the shape B the function V( of a fiat "hill" between Q = 0 and Q ---E o, while the other terms are mainly used for normalization. L is substantially constructed by the Landau distribution, where additionally the width (by *L) and the gradient (by i) are variable. The factor ~[Eo - Q/20. ensures that L = 0 for Q = Eo. The parts of the function were constructed in the following way (all energies in MeV):
__1 G(Q, Eo, 0.) d Q - " g ~ e x p
0.85s
= E, 2000/d
arc
for E,p ~ 0.8 MeV,
(0.859 c x p [ - 0.946(E,,p-(,.6872)21) g =
s
for 0.8 MeV < Eop ~; 1.9 MeV. {17.2 exp( - 2.30 Eop) }s
Eop > O.0760Eop)g, for
t = (0.0147 +
1.9 MeV,
b - 0.186 exp( - 0.413Eop ) s, c = 0.3 + 1000 e x p ( - 3 E o p ) , + 0.1606)512)s,
-
T(Q, Eo, 0.) dQ
1 + a L exp( - 0.435E~p)
i=
0
1 > -At,
else.
The parameters and functions which depend on E o and d are as follows:
2(2.50.)3/2~/Eo-Q
1
parameters which depend on E,¢ approximated by:
( ( Q - E°)Z ) (4)
=t
663
~
( E o - Q ) dQ exp
1
for 0 < Q < Eo, for Q > Eo,
0
exp(u in u + ALU) du,
~(aL) = T~i -i~+c
2.5o"
AL=( Q-2~k°~a + ln(~)--(0.4228--f12))/o'L,
(5) dA =
B(Q, Eo) dQ
1
dQ,
do. L
a = 1.78 x 10-~d//32, 2 = b
0.L = 1.67 + 1197 e x p ( - 6 . 1 7 E o ) ,
+c 1
Eo
13= v/c,
dO
~"-Ekorr = 2.33dA--E[ 1 + 0.42 e x p ( - E o ) ],
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0"1535Zpl ( moc2~2Eo )
for 0 < Q < E o, else,
0
AE=
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(6) L ( Q , E o, 0.) d Q ¢t~(~.L) d A
= il
~/
E o - 20. < Q _
0
Q > Eo.
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+1
0 < Q _
+
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-
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(7) The variable Q corresponds to the energy calibrated pulse height. The input parameters are: E o = incident energy, 0. = 1/2.35 x F W H M of the full energy peak, s = sum of counts with E > 0.37 MeV, dQ = channel width of the experimental spectrum to compare in MeV, d = thickness of the detector in Ixm. The
A subroutine to calculate the Landau density distribution ~(A L) is available e.g. in the program library CERNLIB [23]. A E corresponds to the mean collision energy loss [1,2,6,71, and Z -- 14, P -- 2.33, I = 12.3 eV for silicon. The determination of the fit parameters was done as follows: The total function R was fitted to the measured electron spectra using the partial functions G, 7", B, and L given by eqs. (4)-(7). Then one fit
664
Th. FrommhoM et al. / Response functions of Si detectors
Acknowledgements t04
~r
~ - = 0 91 MeV
experiment
I
J
1 The authors thank Prof. W. Weidlich, E. Lehmann and R. Gauder from the University of Stuttgart for kindly supplying the Monte Carlo program. Thanks arc due to the Giessen linac team for their support during the experiments. The financial support by the Deutsche Forschungsgemcinschaft is gratefully acknowledged.
1oI _ L _ l _ _ . t _ _ ~ t ~ = l
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[2] H.-W. Thiimmel, Durchgang yon Elektronen und Betastrahlung durch Materieschichten (Akademie-Verlag, Berlin, 1974). [31 Glenn F. Knoll, Radiation Detection and Measurement
,ll,J~
2.0
1.5 ;
[I] MJ. Berger, S.M. Seltzer, S.E. Chappell, J.C. Humphreys and J.W. Motz, Nucl. Instr. and Meth. 69 (1969) 181.
. . . .
]
. . . .
i
;
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l0 8
(Wiley, New York, 1979).
[41 K. Siegbahn, Alpha-, Beta- and Gamma-Ray Spectroscopy (North-Holland, Amsterdam, 1966). [51 H.A. Bethe, Ann. Phys. 5 (1930) 325. [6] F. Rohrlich and B. Carlson, Phys. Rev. 93 (1954) 38. [~I M.J. Berger and S.M. Seltzer, NASA-SP-3012 (1964); NAS-NRC 1133 (1965) 205.
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i
3
E n e r g y [MeV] Fig. 9. Comparison of measured response functions for electrons with the approximation by the parametrized analytic function. Upper part: response function for electrons of 0.90 MeV. Middle part: electrons of 1.92 MeV and shapes of the different contributions to the analytic function. Lower part: response function for electrons of 3.50 MeV. parameter was plotted as a function of the bombarding energy E 0 and fitted itself by a suitable function. Then this parameter was fixed in R and R was fitted again. The other fit parameters were handled in an analogous way, until only the input parameters E 0, tr, s, and dQ remained. The parameter E o was replaced by E o p = E o 2000/d, since the mean range of the electrons is approximately proportional to the bombarding energy. E 0 and d are used independently (exact values) only for the calculation of the energy loss peak. So, for detectors with different thicknesses the response function can be determined too. Because of the approximations mentioned, deviations are to be expected for detector thicknesses which are very different from 2900 ~.trn. For three different energies the parametrization is compared with the experimental spectra in fig. 9. In the E o = 1.92 MeV spectrum the four partial functions G, T, B, and L, are plotted separately. The examples presented in the figure show a good agreement between the approximation by the analytic formula and the experimental results.
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