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Pulse height defect of energetic heavy ions in ion-implanted Si detectors
N-R INSTRUMENTS
8METNoos IN PNVSICS ELSEWER
Nuclear
instruments
and Methods
in Physics
Research
A 405 (1998) 39.--44
Pulse height defect of energetic heavy ions in ion-implanted Si detectors G. Pasquali”q*, G. Casini”, M. Bini”, S. Calamai”, A. Olmi”, G. Poggi”, A.A. Stefanini”, F. Saint-Laurentb, J.C. Steckmeyer”
Received 23 July 1997
Abstract The pulse height defect in ion-implanted silicon detectors for elastically scattered ‘“Nb, “‘MO. “%I, ““Sn and ““Xe ions, at energies ranging from about 4 to 25 A MeV has been measured. The results are compared with two widely used parametrizations taken from the literature. !c, 1998 Elsevier Science B.V. All rights reserved.
1. Introduction
In the last few years, our group has studied in detail 2-, 3- and 4-body events in dissipative collisions of heavy ions (A z 100) at intermediate energies [l-4]. In a recent measurement, aimed at studying the excitation energy sharing between the partners of a dissipative collision, our apparatus, based on position sensitive parallel plate avalanche detectors, was supplemented with thick (300 and 500 urn) silicon detectors. The sihcon detectors were placed behind the gas detectors in order to measure the kinetic energy of the heavy fragments, The idea was to compare the pre-evaporative mass (deduced from the kinematics) and the post-evapor-
*Corresponding 229330.
author.
Tel.:
+ 39 55 23075:
fax:
c 39 55
016~-9~~~9~/$19.00 ,(_‘, 1998 Elsevier Science B.V. All rights reserved Pfl s~16~-9002~97)01174-1
ative mass (from the energy and time-of-flight measurements) in order to estimate the excitation energy of the primary fragment. Some results of this investigation have already been reported in Ref. [4]. It is well known that the pulse height produced by a heavy ion in a silicon detector is smaller than that of a light ion depositing the same energy in the detector; this effect is usually referred to as “pulse height defect” (PHD) and must be taken into account in silicon detector caIibrations [S-S]. The pulse height defect is usually defined with respect to alpha particles, so that the “true” energy E of a heavy ion can be separated into two terms: its “apparent” energy E,, which is the energy of an alpha particle yielding the same pulse height, and its “energy defect” AE, defined as E - E,. Since the pulse height produced by the ion is a measure of its kinetic energy, the terms “pulse height defect” and
40
G’. Pusyuuli et al. /Nucl. lnstr. und Mrih. in Phj:r. Rex A JO5 (1YW) 39-44
“energy defect” (BE) will be used interchangeably in the following. In practice, the “true” ion energy is obtained as E, + AE, where E, is derived from a calibration of the detector obtained extrapolating the energies of alpha particles from a radioactive source by means of a precision pulse generator. Therefore, a reliable parametrization of AE as a function of ion mass, atomic number and kinetic energy is needed to derive the total kinetic energy of the stopped ions from the measured pulse height with an uncertainty at the percent level or better. The energy defect AE is often interpreted as the sum of three contributions: the window defect AE,, corresponding to the energy lost by the ion in the dead Iayer at the detector surface, the nuclear stopping defect AE,, corresponding to the energy lost by non-ionizing collisions with lattice atoms, and a residual defect AE,, usually attributed to the recombination of electron-hole pairs along the ionization track. The energy defect, for ions of fixed atomic and mass number, is more important (amounting up to a few percents of the deposited energy) when the whole ion energy is deposited in the silicon, since both charge recombination and non-ionizing collisions are mainly end-of-range effects. The charge recombination is an increasing function of the ionization density, thus it is expected to be relatively more important near the Bragg-peak when the ion has substantially slowed down. The nonionizing collisions, whose contribution can be calculated in the framework of the LSS stopping theory [9], only come into play when the ions are slower than 0.3 A MeV, for the ions considered in the present paper (see Ref. [SJ for a simplified calculation). Investigations of the pulse-height response of silicon detectors to heavy ions at energies of few A MeV have been pursued in the past and some parametrization schemes have been proposed (see, for instance, Refs. [7,8]). Nevertheless, published literature lacks experimental data referring to PHD at the higher energies (few tens of A MeV) which are of interest to us. Moreover, the detectors employed in our apparatus are of the ion-implanted type while available data refer to surface-barrier silicon detectors. Though a systematic study of PHD was beyond the scope of our experiment, an estimate of PHD in
our detectors was possible for elastically scattered ions, whose energies could be reliably determined. Section 2 describes the features of our experimental setup relevant to PHD determination (see Refs. [2-4] for more detailed information on the whole apparatus). The calibration procedure for silicon detectors is described in Section 3. Section 4 refers to the estimate of the “true” energy of elastically scattered ions impinging on a given silicon detector. Experimental PHD values are presented in Section 5, in which they are also compared with the values obtained from the parametrization schemes of Refs. [7,8]. Section 6 contains a brief summary of our tindings.
2. Experimental setup The data presented here refer to the foilowing projectile-target combinations and beam energies: 1. 7 _. 3. 4 5: 6.
r2%n + “‘MO at 4.7 A MeV and at 14 A MeV, “‘MO + “‘Sn at 14AMeV, 93Nb + 93Nb at 3.9 A MeV, 12”Xe + 58Ni at 6.7 A MeV, 93Nb + 93Nb at 25 A MeV, r”%n + 93Nb at 25AMeV.
The measurements related to the first two reactions were performed at the Unilac accelerator of GSI-Darmstadt, the others were performed at GANIL. Most of the silicon detectors were placed below the grazing angle for all the studied reactions, namely, at laboratory polar angles ranging from about 4” to about 11” at Unilac and from about 2” to about 5” at GANIL. Two different silicon detectors arrays were used: the one employed at Unilac consisted of 28 chips with 10 x 10 mm’ active area and 14 chips with 28 x 28mm2 active area manufactured by Hamamatsu Photonics; the nominal active thickness of the detectors was 300pm. The array employed at GANIL consisted of 18 chips with 28 x 28mm’ active area manufactured by Hamamatsu Photonics and 18 chips of 30 x 30mm’ active area manufactured by Eurisys Mesures; the nominal active thickness was 500pm to accommodate the higher energies employed at GANIL.
The nominal full depletion voltage of the detectors was 70 V (100 V) and the nominal resistivity was about 4 kQcm (8 kQcm) for the 300pm (5~~rn) thick chips. During beam time, the bias voltage of the detectors was kept slightly higher (by about 20%) than their full depletion voltage. Continuous compensation for the voltage drop associated with detectors bias current was performed all throughout the measurement. The signals from the detectors were treated by a standard electronic chain: a charge preamplifier followed by a CK - RC” shaping amplifier (7 = 1 J.IS)feeding a peak sensing ADC.
3. Silicon detectors calibrations The energy calibration of the silicon detectors and of the associated electronics, which provides the energy E, (see Section l), was obtained injecting known amounts of charge in the preamplifier input by means of a precision pulser and a reference capacitor. The calibrations have been done both at the beginning and at the end of the experiments. The pulser and reference-capacitor combination had been energy calibrated by comparison with the response of a silicon detector to 31particles from a “mixed nuclides” source [lo]. The 28 x 28mm’ active area detector used for the calibration was one of those employed in the experiment. The energy losses of the alpha particles in the source and in the dead layer of the detector were estimated from the change in pulse height when varying the angle of emergence from the source and the angle of incidence on the detector, respectively. The estimated ‘*normal incidence” values for alphas of 5.8 MeV kinetic energy were 5 keV for the energy lost in the source and 26 keV for the energy lost in the detector entrance window: the uncertainty on those values amounts to few keV. The relative uncertainty on the energy calibration of the pulser is estimated to be of the order of 0.5% or better in the energy range of interest. From the energy lost by alpha particles in the entrance window of the detectors we estimate that the dead layers amount to about 50pg/cm2 for the detectors manufactured by Hamamatsu Photonics and TS ltg/crn’ silicon equivalent for the detectors
manufactured by Eurisys Mesures. These figures compare reasonably well with the manufacturers specifications. A straight line was found to satisfactorily iit the pulse-height characteristics of the eIectronics, the integral non-linearity being less than 1_0.02% in the pulse-height range of interest. Two reference pulser signals of different amplitudes (about onethird and two-thirds of the whole dynamic range) were fed to the test input of the charge preamplifiers both during the calibration procedure and the inbeam measurements. It was then possible to correct for slope and offset variations whenever a drift of the reference peaks was noticed. Besides, the presence of the two reference signals made it possible to correct the charge calibration for the gain change ( < 0.2%) observed in the calibration procedure due to the stray capacitance of the cabie connecting the reference-capacitor to the preamplifier input (20cm. RG174). After calibration, from the centroid of the fullenergy peaks in the pulse-height spectra one can extract the E, values. However. since channeling effects alter the shape of the full-energy peak in the energy spectra. producing shoulders on the right side of the “unchanneled” peak and sometimes even a secondary peak few MeV on the right of the primary peak, the value E, has been calculated from the centroid of the unchanneled peak whenever a sizeable distortion was present. (See Ref. [ 1l] for a study of channeling effects in the silicon detectors employed in our apparatus.)
4. Estimate of the deposited energy At GSI the beam energy was derived from the machine parameters while at GANIL the beam energy was obtained from the beam rigidity. measured by the “Alpha” spectrometer. The relative uncertainty on the beam energy is of the order of O.l”% or better in both cases. The energy of the elastically scattered ions actually deposited in the active region of the detector, was calculated starting from the known beam energy, with the following procedure: 1. the energy A& lost in the target is subtracted from the known beam energy (targets of about
42
200ug/cm2 thickness were used); the value AE, does not appreciably depend on the location of the scattering center within the target thickness. due to the small emission angles of the ions elastically scattered into our detectors; from the scattering angle measured by the position-sensitive gas detector placed in front of the silicon detector, the energy of the ion after Rutherford scattering is calculated; the energy AE,, lost in passing through the gas detector (total thickness of about 800)rg/cm2, mylar equivalent) is subtracted from the ion energy; the energy AE, lost in the entrance window of the silicon detector is subtracted from the ion energy.
employed, mainly because of the different values obtained for A&,,, as shown in Table 1. The energy loss values from Ref. 1133 are claimed to better reproduce the experimental stopping powers, in particular. those of heavy ions of few A MeV in light absorbers such as carbon (see, for instance, Fig. 5 in Ref. [14]): therefore, in the following we will report PHD values estimated using the parametrization of Ref. [13]. The difference between these values and those obtained using Ref. [12] can be easily estimated from the values in Table 1. The uncertainty on the stopping power values introduces substantial uncertainties only at the lowest beam energies.
5. Results The values of these corrections are shown in Table 1. They are representative of all the detectors, since the decrease in incident energy from the smallest to the highest polar angle is. in the adopted experimental setup, less than 4% of the total incident energy. The most significant corrections are associated with the energy AE,, lost in the gas detectors. To evaluate this correction. as well as all other energy losses, we used the stopping power values of Ziegler [12] and those of Hubert et al. 17131.At the lowest energies of this work, the final PHD values depend significantly on the particular energy loss table
The dispersion of PHD values observed for all detectors. expressed as standard deviation CI,was less than 15% for all the studied reactions: Fig. 1 shows, as an example, the PHD values obtained for “‘Sn at 25 A MeV. Dotted lines in Fig. 1 refer to the average value (PHD) and to (PHD) f a(o z 4 MeV). The abscissa identifies different silicon detectors: the polar angles of silicons numbered 1-18 are the same of those numbered 21-38, respectively. The detectors manufactured by Hamamatsu Photonics (numbered l-9
Table 1 Corrections applied to ion energy due to dead layers. calculated from Ref. [ 131tin parenthesis values calculated from Ref. [I 21). All values are in MeV. E is the energy after Rutherford scattering not corrected for loss in the target and refers to the detectors placed at the smallest laboratory polar angles. In the rightmost column the average PHD value obtained for each reaction is reported ION
E
AK
Ah,
A%
PHD
359 563 859 1403 1674 2316 ,883
6.0(5.9) 8.4(8.2) 19118) 4.5(4.6) 6.5(6.6) 4.7f4.9) 6.5t6.8)
56(46) 70(56) 70(58) 34(32) 45(Q) 23t23) 32(32)
2.322) 3.7t3.2) 3.3G.9) 1.9(1,9) 2.5t2.4) 1.2(1.2) 1.6(1.6)
9 15 31
11 29 18 43
PHD values for different silicon detectors FIN. 1. Experimental fcircles: Hamamatsu, squares: Eurisys). The abscissa identities different silicon chips. Dotted lines: average value and average values plus/minus the standard deviation. Data refer to the reaction “‘Sn + “-‘Nb at 25 A MeV.
and 21-29, and represented by circles in the figure) were placed at laboratory polar angles going from about Y’ to about 4”, increasing with the detector number. The detectors manufactured by Eurisys Mesures (squares) were placed at polar angles ranging from about 4” to about 5”. Fig. 2 shows, as a function of incident energy, PI-ID values averaged on all the detectors. The error bars include the standard deviation of the PHD distribution and the 0.5% uncertainty associated with the energy calibration of the detectors. During the ’ “Sn runs - the last ones performed at GANIL - the PHD was found to increase at an approximately constant rate for each detector: after few days of irradiation, the increase was as much as 15 MeV for the detectors placed at about 2” and less than 5 MeV for those placed at about 5”. The rate at which Sn ions hit the detectors ranged from 150 Hz for those placed at about 2” to 6 Hz for those placed at 5”. corresponding to a total dose of about 2.7 x 10’ and 1.2 x 10” incident ions, respectively. For ’ lhSn at 25 A MeV, the plotted value (about 43 MeV) refers to the beginning of the tin runs. The smaller irradiation experienced by detectors placed at larger polar angles may also be responsible for the observed slight decrease in PHD values with increasing silicon number (circles in Fig. 1). More-
over, one cannot exclude in the observed behaviour a possible contribution of channeling effects [ 111, which are expected to be larger for Hamamatsu chips (cut along the { 111) plane) than for Eurisys chips (cut at 7” with respect to the { 111) plane). Since we subtracted the energy lost in the entrance window (A&) from the “true” incident energy, the PHD values of Fig. 2 could be interpreted as the sum of the two terms AE, and AE, (see Section 1). The nuclear stopping defect AE, can be estimated in the framework of the LSS theory. for instance using the simplified formula of Ref. [S]: its contribution amounts to about 2 MeV for Nb and MO, 3 MeV for Sn, 4 MeV for Xe. The solid curves in Fig. 2 are calculated from the empirical parametrization of Ref. [7] where the dependence of PHD (not including AE,.) from the incident energy and the atomic number of the ion is expressed by the formula PHD = lOhE”
(1)
with a and h given, as a function of atomic number, by Q(Z) = 2.230 x 10p’Z2 + 0.5682,
(2)
h(Z) = - 14.252-’
(3)
+ 0.0825.
It is clear from Fig. 2 that Eq. (1). with the parameters u and h defined as in the original work, greatly overestimates the data. Following the method of Ref. [7], we tried to fit the h dependence on atomic number in Eq. (1) to reproduce our PHD values, obtaining for our ions and energies a rather different value of the coefficients: h(Z) = - X5Z-’ + 1.28. Using these values, all the experimental PHI) values were reproduced within the experimental uncertainties. The dashed curves in Fig. 2 are calculated using the parametrization of Ref. [S], which has the form:
Fig. 2. PHD values, averaged on all detectors, as a function of incident energy. Symbols: experimental data; error bars represent the standard deviation plus the contribution of the 0.5% uncertainty on the absolute energy calibration. Solid curves: PHD parametrization of Ref. [7] (for Nb and Sn). Dashed curves: PHD parametrization of Ref. [S] (for 93Nb and r20Sn).
(4) where E is the incident ion energy in MeV, A and Z are the ion mass and atomic number respectively, S is the specific energy loss of the ion in the silicon
in MeV/(mg/cm’), p is the silicon resistivity in Qcm, Feff is the effective electric field strength, in V/cm, at the centroid of the ionized track produced by the ion. The PHD as fitted by Eq. (4) contains the window defect BE, in the entrance window of the surface barrier detectors employed in Ref. [8] (i.e. a gold layer of 40 ug/cm’ and a silicon layer of 8 ug/cm’): in order to compare Eq. (4) with our data we have subtracted from the values obtained using Eq. (4) the AE, contribution, calculated from the reported window thickness of the detectors employed by the authors of Ref. [8]. The second term in square parenthesis contains the dependence on the detector characteristics, resistivity and effective field, and on the specific energy loss of the ion. It was introduced in Ref. [S] by analogy with a model for electron-hole recombination in the plasma formed along the ionization track of the ion. However, the formula was empirically “tuned” by the authors to reproduce their experimentally measured PHD values. In our case, the detector dependent term contributes for less than 6% to the overall PHD for incident energies greater than about 10A MeV. Eq. (4) for 93Nb and “‘Sn ions is in reasonable agreement with our data for 93Nb (“‘MO) and for 12’Sn (’ “Sri) ions, respectively. The calculated PHD value for iz9Xe (not shown) underestimates the experimental value by about 8 MeV. The obtained result gives us a reasonable confidence that all fragments produced in the investigated collisions at 14 and 25 A MeV can be reasonably corrected for PHD effects employing the parametrization of Ref. [X3.
6. Summary We estimated the pulse height defect for 9”Nb rl “‘MO. ““Sri, “‘Sn and 129Xe ions, at energies ranging from about 4 A MeV to 25 A MeV, in a set of about 80 ion-implanted silicon detectors. Dispersion of PHD values for all detectors amounted to less than about 15%. We compared
our data with the empirical parametrizations of Refs. [7,8], which are both based on experimental data at quite lower incident energies ( < 160 MeV). The former overestimates the experimental values, while the latter seems to better reproduce the PHD values for heavy ions in the mass range A = 90-l 30 at intermediate energies.
Acknowledgements We would like to thank the UNILAC accelerator staff of GSI-Darmstadt and the GANIL accelerator staff for having provided excellent beams. Thanks are also due to Mr. R. Ciaranfi and Mr. M. Montecchi for having accurately developed and assembled the preamplifiers and shaper amplifiers used with the silicon detectors and to Mr. F. Maletta for his skilful help during the preparation of the experiments. Useful discussions with M.F. Rivet and B. Borderie are also gratefully acknowledged.
References [I] G. Casini
et al.. Phys. Rev. Lett. 67 (1991) 3364. R.J. Charity et al.. %eit. Phys. A 341 (1991) 53. A.A. Stefanini et al.. Zeit. Phys. A 351 (1995) t67. M G. Casini et al.. Phys. Rev. Lett. 78 (1997) 828. c51 B.D. Wilkins, M.J. Fluss, S.B. Kaufman. C.E. Gross. E.P. Steinberg, Nucl. Instr. and Meth. 92 (1971) 381. 161 S.B. Kaufman. E.P. Steinberg, B.D. Wilkins, J. Unik. A.J. Gorski. Nucl. Instr. and Meth. 115 (1974) 47. R.P. Schmitt, G.J. Wozc71 J.B. Moulton, J.E. Stephenson. niak. Nucl. Instr. and Meth. I57 (1978) 325. 181 M. Ogihara, Y. Nagashima. W. Cinlster. T. Mikumo. Nucl. Instr. and Meth. A 251 (1986) 313. c91 J. Lindhard. V. Nielsen, M. Scharff, P.V. Thomsen, Mat. Fys. Medd. Dan. Vid. Selsk. 33 (IO) (1963) I. UOI Mixed Nuclides. AMR.33. Amersham. C111G. Poggi et al.. Nud. Instr. and Meth. B 119 (1996) 375. Cl’1 J.F. Ziegler. The Stopping and Ranges of Ions in Matter. vol. 4. Pergamon Press, New York. 1997. t131 F. Hubert, R. Bimbot, H. Gauvin. At. Data Nucl. Data Tables 46 ( 1990) 1. Cl41 R. Bimbot. Nucl. Instr. and Meth. B 69 (1992) I.
[S j
8METNoos IN PNVSICS ELSEWER
Nuclear
instruments
and Methods
in Physics
Research
A 405 (1998) 39.--44
Pulse height defect of energetic heavy ions in ion-implanted Si detectors G. Pasquali”q*, G. Casini”, M. Bini”, S. Calamai”, A. Olmi”, G. Poggi”, A.A. Stefanini”, F. Saint-Laurentb, J.C. Steckmeyer”
Received 23 July 1997
Abstract The pulse height defect in ion-implanted silicon detectors for elastically scattered ‘“Nb, “‘MO. “%I, ““Sn and ““Xe ions, at energies ranging from about 4 to 25 A MeV has been measured. The results are compared with two widely used parametrizations taken from the literature. !c, 1998 Elsevier Science B.V. All rights reserved.
1. Introduction
In the last few years, our group has studied in detail 2-, 3- and 4-body events in dissipative collisions of heavy ions (A z 100) at intermediate energies [l-4]. In a recent measurement, aimed at studying the excitation energy sharing between the partners of a dissipative collision, our apparatus, based on position sensitive parallel plate avalanche detectors, was supplemented with thick (300 and 500 urn) silicon detectors. The sihcon detectors were placed behind the gas detectors in order to measure the kinetic energy of the heavy fragments, The idea was to compare the pre-evaporative mass (deduced from the kinematics) and the post-evapor-
*Corresponding 229330.
author.
Tel.:
+ 39 55 23075:
fax:
c 39 55
016~-9~~~9~/$19.00 ,(_‘, 1998 Elsevier Science B.V. All rights reserved Pfl s~16~-9002~97)01174-1
ative mass (from the energy and time-of-flight measurements) in order to estimate the excitation energy of the primary fragment. Some results of this investigation have already been reported in Ref. [4]. It is well known that the pulse height produced by a heavy ion in a silicon detector is smaller than that of a light ion depositing the same energy in the detector; this effect is usually referred to as “pulse height defect” (PHD) and must be taken into account in silicon detector caIibrations [S-S]. The pulse height defect is usually defined with respect to alpha particles, so that the “true” energy E of a heavy ion can be separated into two terms: its “apparent” energy E,, which is the energy of an alpha particle yielding the same pulse height, and its “energy defect” AE, defined as E - E,. Since the pulse height produced by the ion is a measure of its kinetic energy, the terms “pulse height defect” and
40
G’. Pusyuuli et al. /Nucl. lnstr. und Mrih. in Phj:r. Rex A JO5 (1YW) 39-44
“energy defect” (BE) will be used interchangeably in the following. In practice, the “true” ion energy is obtained as E, + AE, where E, is derived from a calibration of the detector obtained extrapolating the energies of alpha particles from a radioactive source by means of a precision pulse generator. Therefore, a reliable parametrization of AE as a function of ion mass, atomic number and kinetic energy is needed to derive the total kinetic energy of the stopped ions from the measured pulse height with an uncertainty at the percent level or better. The energy defect AE is often interpreted as the sum of three contributions: the window defect AE,, corresponding to the energy lost by the ion in the dead Iayer at the detector surface, the nuclear stopping defect AE,, corresponding to the energy lost by non-ionizing collisions with lattice atoms, and a residual defect AE,, usually attributed to the recombination of electron-hole pairs along the ionization track. The energy defect, for ions of fixed atomic and mass number, is more important (amounting up to a few percents of the deposited energy) when the whole ion energy is deposited in the silicon, since both charge recombination and non-ionizing collisions are mainly end-of-range effects. The charge recombination is an increasing function of the ionization density, thus it is expected to be relatively more important near the Bragg-peak when the ion has substantially slowed down. The nonionizing collisions, whose contribution can be calculated in the framework of the LSS stopping theory [9], only come into play when the ions are slower than 0.3 A MeV, for the ions considered in the present paper (see Ref. [SJ for a simplified calculation). Investigations of the pulse-height response of silicon detectors to heavy ions at energies of few A MeV have been pursued in the past and some parametrization schemes have been proposed (see, for instance, Refs. [7,8]). Nevertheless, published literature lacks experimental data referring to PHD at the higher energies (few tens of A MeV) which are of interest to us. Moreover, the detectors employed in our apparatus are of the ion-implanted type while available data refer to surface-barrier silicon detectors. Though a systematic study of PHD was beyond the scope of our experiment, an estimate of PHD in
our detectors was possible for elastically scattered ions, whose energies could be reliably determined. Section 2 describes the features of our experimental setup relevant to PHD determination (see Refs. [2-4] for more detailed information on the whole apparatus). The calibration procedure for silicon detectors is described in Section 3. Section 4 refers to the estimate of the “true” energy of elastically scattered ions impinging on a given silicon detector. Experimental PHD values are presented in Section 5, in which they are also compared with the values obtained from the parametrization schemes of Refs. [7,8]. Section 6 contains a brief summary of our tindings.
2. Experimental setup The data presented here refer to the foilowing projectile-target combinations and beam energies: 1. 7 _. 3. 4 5: 6.
r2%n + “‘MO at 4.7 A MeV and at 14 A MeV, “‘MO + “‘Sn at 14AMeV, 93Nb + 93Nb at 3.9 A MeV, 12”Xe + 58Ni at 6.7 A MeV, 93Nb + 93Nb at 25 A MeV, r”%n + 93Nb at 25AMeV.
The measurements related to the first two reactions were performed at the Unilac accelerator of GSI-Darmstadt, the others were performed at GANIL. Most of the silicon detectors were placed below the grazing angle for all the studied reactions, namely, at laboratory polar angles ranging from about 4” to about 11” at Unilac and from about 2” to about 5” at GANIL. Two different silicon detectors arrays were used: the one employed at Unilac consisted of 28 chips with 10 x 10 mm’ active area and 14 chips with 28 x 28mm2 active area manufactured by Hamamatsu Photonics; the nominal active thickness of the detectors was 300pm. The array employed at GANIL consisted of 18 chips with 28 x 28mm’ active area manufactured by Hamamatsu Photonics and 18 chips of 30 x 30mm’ active area manufactured by Eurisys Mesures; the nominal active thickness was 500pm to accommodate the higher energies employed at GANIL.
The nominal full depletion voltage of the detectors was 70 V (100 V) and the nominal resistivity was about 4 kQcm (8 kQcm) for the 300pm (5~~rn) thick chips. During beam time, the bias voltage of the detectors was kept slightly higher (by about 20%) than their full depletion voltage. Continuous compensation for the voltage drop associated with detectors bias current was performed all throughout the measurement. The signals from the detectors were treated by a standard electronic chain: a charge preamplifier followed by a CK - RC” shaping amplifier (7 = 1 J.IS)feeding a peak sensing ADC.
3. Silicon detectors calibrations The energy calibration of the silicon detectors and of the associated electronics, which provides the energy E, (see Section l), was obtained injecting known amounts of charge in the preamplifier input by means of a precision pulser and a reference capacitor. The calibrations have been done both at the beginning and at the end of the experiments. The pulser and reference-capacitor combination had been energy calibrated by comparison with the response of a silicon detector to 31particles from a “mixed nuclides” source [lo]. The 28 x 28mm’ active area detector used for the calibration was one of those employed in the experiment. The energy losses of the alpha particles in the source and in the dead layer of the detector were estimated from the change in pulse height when varying the angle of emergence from the source and the angle of incidence on the detector, respectively. The estimated ‘*normal incidence” values for alphas of 5.8 MeV kinetic energy were 5 keV for the energy lost in the source and 26 keV for the energy lost in the detector entrance window: the uncertainty on those values amounts to few keV. The relative uncertainty on the energy calibration of the pulser is estimated to be of the order of 0.5% or better in the energy range of interest. From the energy lost by alpha particles in the entrance window of the detectors we estimate that the dead layers amount to about 50pg/cm2 for the detectors manufactured by Hamamatsu Photonics and TS ltg/crn’ silicon equivalent for the detectors
manufactured by Eurisys Mesures. These figures compare reasonably well with the manufacturers specifications. A straight line was found to satisfactorily iit the pulse-height characteristics of the eIectronics, the integral non-linearity being less than 1_0.02% in the pulse-height range of interest. Two reference pulser signals of different amplitudes (about onethird and two-thirds of the whole dynamic range) were fed to the test input of the charge preamplifiers both during the calibration procedure and the inbeam measurements. It was then possible to correct for slope and offset variations whenever a drift of the reference peaks was noticed. Besides, the presence of the two reference signals made it possible to correct the charge calibration for the gain change ( < 0.2%) observed in the calibration procedure due to the stray capacitance of the cabie connecting the reference-capacitor to the preamplifier input (20cm. RG174). After calibration, from the centroid of the fullenergy peaks in the pulse-height spectra one can extract the E, values. However. since channeling effects alter the shape of the full-energy peak in the energy spectra. producing shoulders on the right side of the “unchanneled” peak and sometimes even a secondary peak few MeV on the right of the primary peak, the value E, has been calculated from the centroid of the unchanneled peak whenever a sizeable distortion was present. (See Ref. [ 1l] for a study of channeling effects in the silicon detectors employed in our apparatus.)
4. Estimate of the deposited energy At GSI the beam energy was derived from the machine parameters while at GANIL the beam energy was obtained from the beam rigidity. measured by the “Alpha” spectrometer. The relative uncertainty on the beam energy is of the order of O.l”% or better in both cases. The energy of the elastically scattered ions actually deposited in the active region of the detector, was calculated starting from the known beam energy, with the following procedure: 1. the energy A& lost in the target is subtracted from the known beam energy (targets of about
42
200ug/cm2 thickness were used); the value AE, does not appreciably depend on the location of the scattering center within the target thickness. due to the small emission angles of the ions elastically scattered into our detectors; from the scattering angle measured by the position-sensitive gas detector placed in front of the silicon detector, the energy of the ion after Rutherford scattering is calculated; the energy AE,, lost in passing through the gas detector (total thickness of about 800)rg/cm2, mylar equivalent) is subtracted from the ion energy; the energy AE, lost in the entrance window of the silicon detector is subtracted from the ion energy.
employed, mainly because of the different values obtained for A&,,, as shown in Table 1. The energy loss values from Ref. 1133 are claimed to better reproduce the experimental stopping powers, in particular. those of heavy ions of few A MeV in light absorbers such as carbon (see, for instance, Fig. 5 in Ref. [14]): therefore, in the following we will report PHD values estimated using the parametrization of Ref. [13]. The difference between these values and those obtained using Ref. [12] can be easily estimated from the values in Table 1. The uncertainty on the stopping power values introduces substantial uncertainties only at the lowest beam energies.
5. Results The values of these corrections are shown in Table 1. They are representative of all the detectors, since the decrease in incident energy from the smallest to the highest polar angle is. in the adopted experimental setup, less than 4% of the total incident energy. The most significant corrections are associated with the energy AE,, lost in the gas detectors. To evaluate this correction. as well as all other energy losses, we used the stopping power values of Ziegler [12] and those of Hubert et al. 17131.At the lowest energies of this work, the final PHD values depend significantly on the particular energy loss table
The dispersion of PHD values observed for all detectors. expressed as standard deviation CI,was less than 15% for all the studied reactions: Fig. 1 shows, as an example, the PHD values obtained for “‘Sn at 25 A MeV. Dotted lines in Fig. 1 refer to the average value (PHD) and to (PHD) f a(o z 4 MeV). The abscissa identifies different silicon detectors: the polar angles of silicons numbered 1-18 are the same of those numbered 21-38, respectively. The detectors manufactured by Hamamatsu Photonics (numbered l-9
Table 1 Corrections applied to ion energy due to dead layers. calculated from Ref. [ 131tin parenthesis values calculated from Ref. [I 21). All values are in MeV. E is the energy after Rutherford scattering not corrected for loss in the target and refers to the detectors placed at the smallest laboratory polar angles. In the rightmost column the average PHD value obtained for each reaction is reported ION
E
AK
Ah,
A%
PHD
359 563 859 1403 1674 2316 ,883
6.0(5.9) 8.4(8.2) 19118) 4.5(4.6) 6.5(6.6) 4.7f4.9) 6.5t6.8)
56(46) 70(56) 70(58) 34(32) 45(Q) 23t23) 32(32)
2.322) 3.7t3.2) 3.3G.9) 1.9(1,9) 2.5t2.4) 1.2(1.2) 1.6(1.6)
9 15 31
11 29 18 43
PHD values for different silicon detectors FIN. 1. Experimental fcircles: Hamamatsu, squares: Eurisys). The abscissa identities different silicon chips. Dotted lines: average value and average values plus/minus the standard deviation. Data refer to the reaction “‘Sn + “-‘Nb at 25 A MeV.
and 21-29, and represented by circles in the figure) were placed at laboratory polar angles going from about Y’ to about 4”, increasing with the detector number. The detectors manufactured by Eurisys Mesures (squares) were placed at polar angles ranging from about 4” to about 5”. Fig. 2 shows, as a function of incident energy, PI-ID values averaged on all the detectors. The error bars include the standard deviation of the PHD distribution and the 0.5% uncertainty associated with the energy calibration of the detectors. During the ’ “Sn runs - the last ones performed at GANIL - the PHD was found to increase at an approximately constant rate for each detector: after few days of irradiation, the increase was as much as 15 MeV for the detectors placed at about 2” and less than 5 MeV for those placed at about 5”. The rate at which Sn ions hit the detectors ranged from 150 Hz for those placed at about 2” to 6 Hz for those placed at 5”. corresponding to a total dose of about 2.7 x 10’ and 1.2 x 10” incident ions, respectively. For ’ lhSn at 25 A MeV, the plotted value (about 43 MeV) refers to the beginning of the tin runs. The smaller irradiation experienced by detectors placed at larger polar angles may also be responsible for the observed slight decrease in PHD values with increasing silicon number (circles in Fig. 1). More-
over, one cannot exclude in the observed behaviour a possible contribution of channeling effects [ 111, which are expected to be larger for Hamamatsu chips (cut along the { 111) plane) than for Eurisys chips (cut at 7” with respect to the { 111) plane). Since we subtracted the energy lost in the entrance window (A&) from the “true” incident energy, the PHD values of Fig. 2 could be interpreted as the sum of the two terms AE, and AE, (see Section 1). The nuclear stopping defect AE, can be estimated in the framework of the LSS theory. for instance using the simplified formula of Ref. [S]: its contribution amounts to about 2 MeV for Nb and MO, 3 MeV for Sn, 4 MeV for Xe. The solid curves in Fig. 2 are calculated from the empirical parametrization of Ref. [7] where the dependence of PHD (not including AE,.) from the incident energy and the atomic number of the ion is expressed by the formula PHD = lOhE”
(1)
with a and h given, as a function of atomic number, by Q(Z) = 2.230 x 10p’Z2 + 0.5682,
(2)
h(Z) = - 14.252-’
(3)
+ 0.0825.
It is clear from Fig. 2 that Eq. (1). with the parameters u and h defined as in the original work, greatly overestimates the data. Following the method of Ref. [7], we tried to fit the h dependence on atomic number in Eq. (1) to reproduce our PHD values, obtaining for our ions and energies a rather different value of the coefficients: h(Z) = - X5Z-’ + 1.28. Using these values, all the experimental PHI) values were reproduced within the experimental uncertainties. The dashed curves in Fig. 2 are calculated using the parametrization of Ref. [S], which has the form:
Fig. 2. PHD values, averaged on all detectors, as a function of incident energy. Symbols: experimental data; error bars represent the standard deviation plus the contribution of the 0.5% uncertainty on the absolute energy calibration. Solid curves: PHD parametrization of Ref. [7] (for Nb and Sn). Dashed curves: PHD parametrization of Ref. [S] (for 93Nb and r20Sn).
(4) where E is the incident ion energy in MeV, A and Z are the ion mass and atomic number respectively, S is the specific energy loss of the ion in the silicon
in MeV/(mg/cm’), p is the silicon resistivity in Qcm, Feff is the effective electric field strength, in V/cm, at the centroid of the ionized track produced by the ion. The PHD as fitted by Eq. (4) contains the window defect BE, in the entrance window of the surface barrier detectors employed in Ref. [8] (i.e. a gold layer of 40 ug/cm’ and a silicon layer of 8 ug/cm’): in order to compare Eq. (4) with our data we have subtracted from the values obtained using Eq. (4) the AE, contribution, calculated from the reported window thickness of the detectors employed by the authors of Ref. [8]. The second term in square parenthesis contains the dependence on the detector characteristics, resistivity and effective field, and on the specific energy loss of the ion. It was introduced in Ref. [S] by analogy with a model for electron-hole recombination in the plasma formed along the ionization track of the ion. However, the formula was empirically “tuned” by the authors to reproduce their experimentally measured PHD values. In our case, the detector dependent term contributes for less than 6% to the overall PHD for incident energies greater than about 10A MeV. Eq. (4) for 93Nb and “‘Sn ions is in reasonable agreement with our data for 93Nb (“‘MO) and for 12’Sn (’ “Sri) ions, respectively. The calculated PHD value for iz9Xe (not shown) underestimates the experimental value by about 8 MeV. The obtained result gives us a reasonable confidence that all fragments produced in the investigated collisions at 14 and 25 A MeV can be reasonably corrected for PHD effects employing the parametrization of Ref. [X3.
6. Summary We estimated the pulse height defect for 9”Nb rl “‘MO. ““Sri, “‘Sn and 129Xe ions, at energies ranging from about 4 A MeV to 25 A MeV, in a set of about 80 ion-implanted silicon detectors. Dispersion of PHD values for all detectors amounted to less than about 15%. We compared
our data with the empirical parametrizations of Refs. [7,8], which are both based on experimental data at quite lower incident energies ( < 160 MeV). The former overestimates the experimental values, while the latter seems to better reproduce the PHD values for heavy ions in the mass range A = 90-l 30 at intermediate energies.
Acknowledgements We would like to thank the UNILAC accelerator staff of GSI-Darmstadt and the GANIL accelerator staff for having provided excellent beams. Thanks are also due to Mr. R. Ciaranfi and Mr. M. Montecchi for having accurately developed and assembled the preamplifiers and shaper amplifiers used with the silicon detectors and to Mr. F. Maletta for his skilful help during the preparation of the experiments. Useful discussions with M.F. Rivet and B. Borderie are also gratefully acknowledged.
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