The influence of plasma effects on the timing properties of surface-barrier detectors for heavy ions

Nuclear Instruments and Methods m Physics Research A240 (1985) 145-151 North-Holland, Amsterdam

145

THE INFLUENCE OF PLASMA EFFECTS ON THE TIMING PROPERTIES OF SURFACE-BARRIER DETECTORS FOR HEAVY IONS W. BOHNE, W. GALSTER *, K . GRABISCH and H. MORGENSTERN

Hahn-Meaner-Institut für Kernforschung Berlin GmbH, D-1000 Berlin 39, Postfach 390128, FRG

Received 29 April 1985 Detecting ions from He to Xe at various accurately determined energies with surface-barrier detectors, the dependence of the timing signal on field strength, resistivity, area and thickness of the detector has been studied. Deviations of the measured time-of-flight from the calculated one in the order of up to several ns have been found for slow heavy ions . A variation of the field strength may also cause a time sluft of several ns, depending on mass and velocity of the detected ions and the properties of the detector. Above a critical field Fm, a linear decrease of this "plasma delay" with increasing field strength has been observed . By linear extrapolation to infinite field strength a value for the minimum charge-collecting time of each detector has been determined . The experimental data allow to extract a set of empirical formulae that are able to describe the "plasma delay" as a function of the energy, mass and effective charge of the detected ions and of the thickness, area and resistivity of the detector .

1. Introduction From previous experimental investigations it is well known that the timing signal obtained from a silicon surface-barrier detector (SBD) does not represent the correct time-of-arrival of an ion in the detector, as it usually is too late [1-6]. This has been explained in terms of the creation of a high conductivity plasma along the particle trajectory which disturbs for some time (plasma time or plasma-decay time) the internal electric field and therefore retards the charge collection [7-9]. This results in an increased rise time of the fast signal . The dependence of the rise time on the field strength and resistivity of the detector and on the ion mass and energy has been studied in the past (see e.g . refs . [7,10,11]). With modern electronics such as constant-fraction discriminators (CFD) it is possible to compensate for these rise-time fluctuations . But, nevertheless, timing signals from heavy fission fragments were registered several ns later than compared to pulses obtained from alpha particles (see e.g . refs . [1,2]) . Although it was shown by Hannappel et al . [3] and by Girard et a] . [12] that there is no real time shift at the onset of detector signals from heavily ionizing particles, we will maintain the perhaps misleading name "plasma delay" for this effect of variation of the time reference

* Present address: Faculty of Science and Technology, University of Tsukuba, Ibaraki 305, Japan . 0168-9002/85/$03 .30 © Elsevier Science Publishers B.V . (North-Holland Physics Publishing Division)

derived from surface-barrier detectors for different ions . Time-of-flight measurements are a widely accepted tool to determine mass and/or velocity of the products following a heavy ion induced reaction . In any case it is necessary to determine the absolute value of the time very precisely. Typically the time zero is obtained from an alpha source or fast elastically scattered ions. Due to the "plasma delay" this value is too low for slow heavy residues or fission fragments and too high for fast lighter reaction products, resulting in an error in the evaluation of mass and velocity . While these problems can be overcome by replacing the surface-barrier detector with a channel-plate array or an avalanche counter, surface-barrier detectors have been extensively used in the past and are a convenient means. In order to find a recipe to correct for the effect of the "plasma delay" in time-of-flight measurements with surface-barrier detectors we carried out a detailed investigation of this effect with good time resolution . To obtain the systematics of the dependence on mass and energy of the detected ions, we not only used alpha particles and fission fragments, as with only few exceptions has been done in the past, but irradiated the detectors with heavy ion beams of different energies in the mass region from He to Xe. Furthermore we used different types of detectors to study the influence of the crystal material . In most cases we performed additional measurements as a function of the detector bias, to determine the dependence of the "plasma delay" on the electric field strength (F) in a wide range (3 _< F 5 30 kV/cm) .

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2. Experimental setup 2.1 . Detector arrangement and calibration

The experiments were performed with the time-offlight spectrometer at the VICKSI facility of the HahnMeitner-Institut, Berlin. Self-supporting thin (< 100 pg/cm2 ) gold targets were bombarded with 12C, 20Ne, 22Ne, 4°Ar, 86 Kr and 129X ions e of energies between 55 and 480 MeV. In addition, alpha particles of 6.05 and 8.78 MeV obtained from a ThC' source mounted in the target position were used. Alpha particles and elastically scattered ions were identified by means of the time-offlight method . The experimental setup is shown schematically in fig. 1 . It consists of a channel-plate array (CP) as start detector at a distance of 35 cm from the target and a mirror-channel-plate array (MCP) and a surface-barrier detector (SBD) both serving as stop detectors. The flight paths between CP and MCP and between CP and SBD were determined very accurately by different geometrical, optical and electronical methods to be (118 .3 ± 0.1) cm and (134 .0 t 0.2) cm, respectively. The secondary electron emitting foils of the channel-plate arrays were made from 12 [tg/cm2 thin Formvar foils coated with 10 tLg/cm2 gold . To calculate the correct time-of-flight it is necessary to know very precisely the energy of the scattered ions. The absolute beam energy is obtained from the calibration of the analyzing magnet to an accuracy of better than 10 -3 [13] . This error is negligible compared to the uncertainty of the energy loss in the target and the detector foils. Therefore we installed a second channel-plate detector (MCP) to measure the velocity, which is slightly reduced due to the energy loss in the target and the foil of the first channel plate. The time calibration was done with a very precise time-pulse generator (PG 42, developed by the electronics department of the Hahn-Meitner-Institute), with a delay cable whose transit time is known to f 10 ps and with the rf of the cyclotron. The time-zero point was obtained by means of the 8.784 MeV alpha particles of a ThC' source . With this method it was

Target 100Ng/CM Z Au Fig. 1. Schematic drawing of the experimental setup.

possible to determine the reduced energy to an accuracy of about 10 -3 (see also sect . 2.2). The remaining uncertainty caused by the energy loss in the foil of the minor-channel-plate is corrected for and contributes only little to the error in the entire time-of-flight, due to the short rest-flight path of 15 .7 cm compared to the total length of 134 cm . Thus the resulting uncertainty of the calculated time-of-flight is also in the order of 10 -3, i.e. in the range of 10--60 ps depending on the time-offlight of the detected ions . A slight inclination of the stop detectors relative to the beam axis is necessary to compensate for the flightpath variation over the entire solid angle, due to an angle of 45° between start detector and ion direction. But the inclination of the ionization track orientation relative to the field in the crystal of the SBD does not affect the charge collection as shown by Girard et al . [12] . 2.2. Electronics setup

The time channels for all three detectors are built up with identical electronic devices. In the case of the SBD we used an additional fast time-pickup and preamplifier system with a rise time of less than 0.6 ns (IV48, developed at the electronics department of the HMI) . The electronics diagram is shown in fig. 2. To avoid a possible remaining time walk of the constant-fraction discriminators (CFD), due to varying pulse heights obtained from different ions, we adjusted the amplitudes of the fast signals for all ions and energies to - 1 V with the aid of fast amplifiers and variable attenuators . The gain of the fast amplifier is variable from 10 to 100, its rise time is less than 1 ns (IV62, development of the electronics department of the HMI). For the Th-a particles, which generate in all detectors the smallest signals, the gain of the amplifier was chosen to obtain -1 V signals with zero attenuation. The signals from heavy ions were reduced to - 1 V by variable 4 GHz attenuators (Kay, model 461 B). The transit-time fluctuations of these attenuators are less than 10 ps, measured with a fast pulse generator with a rise time of 25 ps . Nevertheless, the walk of the following CFDs was carefully adjusted, resulting in a maximum time jitter of the TAC output of t 20 ps for a pulse height variation of ± 10 dB . To test a possible influence on the type of CFD, we used for the same measurement different CFDs (Ortec model 934, Tennelec model 453, Tennelec model 454) . The value of the fraction was 0.2 for all models . In all measurements the time range of the time-toamplitude converters (TAC) were set to 100 ns. The TAC signals were converted by an 8K ADC and stored together with the corresponding energy signal of the SBD event by event on a magnetic disc of an on-line computer, i.e . the sensitivity of the time scale was 12 ps per channel.

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W. Bohne et al. / Influence ofplasma effects on timing properties

Const Fract Discr in

Const Fracf Discnm

Delay

Delay

Fast variable Ampl

Stop

Stop

Start

TAC

POP 11/40

Fig. 2. Schematic representation of the electronics diagram. 3. Measurements The measurements were done with different types of detectors, such as totally depleted, partially depleted

and fission detectors (all from Ortec), and also with the new type of passivated ion implanted siliconjunction detectors (from Schlumberger). The detectors had an active area from 100 to 450 mm2 as normally used in

Table 1 Specifications and measured properties together with the calculated values of the field strength region for all detectors studied Det. number

Specifications from manufacturer

Type a)

Active area [mm2 1

1 2 3 4 5 6 7 8 9

10 11 12 13

BE-17-300-300 BB-20-300-200 BB-18-300-300 TB-20-300-500 TB-25-450-300 BB-20-300-150S TB-25-450-150 TB-20-300-1000 TB-17-150-700

TB-16-100-300 BF-25-300-60 IPT 280-300 b) TD-300-250-20 `)

300 300 300 300 4S0 300 4S0 300 1S0 100 300 280 300

Thickness d [pm]

321 d) 179 319 527 324 161

142 1000 712

304 315 d) 320 2S0

Measured characteristics and computed field strengths Resistivity

p e)

p [S2 cm]

Recommended bias [V]

4700 2300 1800 10000 3900 1S00 8S0 34000 8000

115 140 230 110 130 1S0 100 120 27S

2000

1S0

10S00 ±1800 1600 ±100 n.a. 14400 ±1700 3900 ±400 420 ±100 700 ±150 36000± 3000 8600± 600 23 000 t 3S00 600±70 2400± 4S0 2100± 300

5600 546 3700

12S 110 110

(Sl cm)

Capacitance ` C [pF]

Maximum bias [V]

Field strength g) F [kV/cm]

- Rise time h)

123 t 2 221 t 5 n.a . 78 t 2 174± 5 232 t 2 323 t 8 51±2 35 f 1 52±2 122 t 5 1S5 t 7 148 t 5

660 560 780 96S 720 170 310 660 1160 680 770 180 340

2.7-9 .0 6.6-21.2 8.2-23.6 3.0-9 .3 5.7-15.4 11 .0-22.8 9.6-23.8 2.7-4 .8 5.5-13.2 2.4-6 .2 9.8-40.5 7.3-9 .8 6.1-14.4

3.4-2 .8 3.3-2 .7 3.5-2 .9 4.0-3 .1 3.4-2 .8 2.8-2 .6 3.4-3 .2 4.3-3 .5 3.5-3 .0 3.4-2 .7 3.3-2 .7 3.5-3 .1 3.4-2 .9

a) All detectors from Ortec except nos. 12, 13 . b) From Schlumberger . e)

From Tennelec .

d) Not totally depleted detector, the value is the thickness of the Si slice, according to Ortec. e) Mean value of the resistivity obtained from capacitance and range

measurements (see text). Constant minimum values of the capacitance for totally depleted detectors. g) Minimum and maximum value of the used front-face field strength. h) Signal-rise time for 8.78 MeV a-particles at the lowest and highest field strength, respectively .

tr

Ins]

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W. Bohne et al. / Influence of plasma effects on timing properties

our time-of-flight spectrometer. They were selected to deliver time signals of approximately the same rise time of t, = (3 .1 ± 0.3) ns for alpha particles. For most of the heavier ions we obtained similar rise times if the detectors were operated at a bias of at least the recommended voltage. Only for bias values well below this voltage and for very heavy and slow ions (Xe, Kr) the rise time increased up to a maximum of about 5 ns . (In the case of Xe and very low field strength we measured with one detector of high resistivity a value even of tr = 6 ns .) In table 1 typical values of tr and field strength are listed together with the specifications of the detectors. The measurements were performed with the same setup, i.e. identical electronic modules and cabels . All electronics parameters such as threshold and walk ad justment were kept constant . Due to slightly varying rise times we have to use the CFDs in the amplitude-rise-time compensating mode (ARC mode) [14] even though this deteriorated somewhat the time resolution of the system. The delay of 2.8 ns in the CFDs was kept constant for all detectors, ions and field strengths. The overall time resolution obtained was about 130-180 ps for ions up to At and about 230 ps for Kr and Xe ions . The time-zero calibration for all detectors was done with a ThC' alpha source by varying the field strength F. Already in 1966 Meyer [15] has proposed a linear dependence of the "plasma time" on the inverse field strength . Neidel and Henschel [2] showed that this holds as well for the "plasma delay" and that by an extrapolation to infinitely high field strengths (1/F-> 0) the plasma delay vanishes, at least for light ions. In our arrangement the measured time-of-flight signal T is given by T = To - t where t is the true (calculated) time-of-flight of the ions . To = To" + Tdet + Td includes the electronics delay To" (cabels, modules), a possible basic delay Td" for a given detector and the "plasma delay" Td . With increasing field strength Td should vanish and the extrapolation of the sum of the measured and the calculated time-of-flight for both alpha energies (6.05 and 8.78 MeV) to 1/F=0 should intersect the time axis at a common point: T, . Relative to this value the "plasma delay" for all ions and energies was determined . All measurements were performed at room temperature ((24 f 2)°C). We are aware, however, of a strong dependence of the "plasma time" on the temperature [6,11] . The temperature of the detection electronics was kept constant to within ± 0XC. 4. Results First we want to show the dependence of the time shift on the mean effective field strength Fete using different detectors to stop the a-particles. The values of the effective electric field were calculated for the

centroids x of the ionized tracks . (The charge centroid of the Bragg curve for a-particles is in good approximation 2/3 of the range r according to Ammerlaan et al . [16] .) The field strength F at a given distance x from the front electrode was calculated by the following expression (see e.g. refs. [17-19]) : (d-x), jur 1 where d -- (2TuU)1/2 is the depletion depth at a given bias voltage U, with the electron mobility ,u = 1481 cm2 V -1 s-1 and the electron charge collection time T = EE 0p = p x 10 -12 s, p being the detector resistivity, E the dielectric constant of Si and Eo the free space permittivity. To calculate the field strength it is necessary to know the resistivity p. Unfortunately, it turned out that this quantity may deviate seriously from the specified value, especially for well used detectors. We therefore determined the resistivity of all our detectors by measuring the capacitance as a function of the detector bias . From the constant value of the totally depleted detector and the gradient at lower voltages it is possible to extract the real area and the mean resistivity of the detector crystal with an accuracy of about 10-15% . In F(x) =

Det 6

Det 5

Det 1

1

I

X. _ 02 03 1/ F.ff [cm/kV1

.

I

04

.

Fig. 3. To as a function of the inverse effective field for three different detectors (see table 1) and two a-energies . The lower curve of each detector represents the results obtained with 6.05 MeV a-particles. The arrows indicate the values of Fm, (see text).

W. Bohne et al. / Influence ofplasma effects on timing properties

14 9

5 10

05

4 N C v3 H 2

Fig . 4 . "Plasma-delay" of 8 .78 MeV a-particles vs inverse effective field for different detectors . The arrows indicate Fm, . addition we determined p from the bias dependence of the depletion depth by the aid of the known range of the Th alpha particles . Furthermore transmission detectors were checked by the same method, impinging the detector from the rear with a-particles. Within the errors the results of all three methods are in agreement . The uncertainty is still relatively large due to the variation of the resistivity in the detector crystal (see e.g . ref. [20]) . The averaged values of p are also listed in table 1 . Fig. 3 displays the behaviour of To for three different detectors. In all three cases it is seen that above a certain field strength the time-shifts are linear with 1/Ferf . The two curves (the lower one is for 6 .05 MeV a-particles the upper one for 8 .78 MeV a-particles) assigned to a detector intersect the time scale with good accuracy at the same point, the time-zero point T0'0 *. Apart from having slightly different internal delays for the various detectors the slopes of the curves in fig. 3 also depend on the detector. To compare the curves we display in fig . 4 for the case of the 8 .78 MeV a-particles the "plasma delay" Td , deduced by subtracting To from the corresponding extrapolated value To' . The error bars of about ± 50 ps indicate the relative uncertainties only . The errors involved in evaluating the absolute time scales for the different curves are estimated to be about 100 ps, mainly due to possible errors in the extrapolation to the time axis. Using the time-zero points obtained with a-particles the "plasma delay" of various heavy ions with different energies is determined . As an example fig . 5 shows the field dependence of the "plasma delay" for a-particles, 129Xe ions and °°Ar ions at two different energies in one detector. Many of these "plasma delay" curves were measured, in some cases, however, only at a few different field strengths . The results exhibit the same trend, a linearly decreasing part at high field strengths and in most cases a saturation or even a decrease of the "plasma

05 Fig. 5 . "Plasma-delay" of 8 .78 MeV a-particles, 166 MeV 1i9Xe ions and °°Ar ions of 270 MeV and 480 MeV vs inverse effective field in detector 1 . The arrows indicate Fm, . The straight lines are results of calculations obtained with eqs . (3) and (4) .

delay" at small values of the effective field . Only for very slow ions or in the case where the detector was too thin to stop the ions this saturation was not observed but rather a continuing increase of the "plasma-delay" time with decreasing field . The findings are not affected considerably by the use of different types of constant-fraction discriminators as mentioned already (however, Toe' varies due to different transit times of the various modules) . This is not unexpected . All models involved have the same trigger fraction of 0 .2 and were used with similar lower thresholds . Even a variation of the trigger fraction does not change the results obtained significantly (see, e.g ., also ref. [2]) as long as the corresponding crossover is on the linear part of the fast signal . The general trend observed in our data encouraged us to search for an empirical formula. This was not possible with one expression for the entire range of the electrical field . In order to focus on the main features we divided the curves into two parts . In region I at field strengths above a critical field F,in we observe the well known linear decrease of the "plasma delay" with 1/F. In region II at field strengths below F~n, we assume for the sake of simplicity a linear dependence on I/F as well . We did not attempt to fit the transition region . With the following set of formulae it is possible to reproduce the linear parts of all our measured "plasma delay" curves within the error bars . I F, ..

=

2rMp )1/2 1 d' 10-31 E

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W. Bohne et al. / Influence ojplasma effects on timing properties

01

02 11Fe  [cm1kV]

03

Fig. 6. "Plasma-delay" of some ions vs inverse effective field in different detectors . The position of the arrows indicating Fm,n and the straight lines are calculated with egs.(2)-(4). If

Feff

> Fnnn

(region I):

Td

r _P =Mexp(3J5M)C\d)zFeff /S

If

Feff < Fndn

Td =To

(region II) :

\z _ -sign(d-r')2 .7(Z I In( 2E)exp( 3 .75M) Z /

_ x (Cp) i / z1 Fef

with to =2.8 x 10 -5(Z/M)zCp/rt .z. E (in MeV) is the energy deposited by ionization in the detector, M is the mass of the ion (in amu), Z is the effective charge of the ion (in charge units), d (in cm) is the thickness of the detector crystal, r, r' (in cm) is the range of the ion in Si (if the ion is not stopped in the detector: r = d/2!), is the resistivity of the detector (in Sl cm), P C is the capacitance of the totally depleted detector (in pF) . (In all formulae we use the relatively well determined capacitance instead of the not precisely known area of the detector crystal.) The "plasma delay" is calculated in PS . The range and the effective charge are obtained from range and stopping-power tables [21,22] using the relation [21] Z_

~ (dE/dx) ,on (dE/dX )proton

Jt/Z

with the stopping power dE/dx of the ion and proton at the same velocity. Some of the results obtained with eqs. (2)-(4) are shown in figs. 4-6 as straight lines. The vertical arrows indicate Fm,n, i.e. the validity limit of region I (eq . (2)). The quality of the fits is quite good. Only in the case of detectors with very low resistivity we find significant deviations . These unexpected deviations may arise from

a substantial uncertainty in the time-zero extrapolation . If p is in the order of hundred Sl cm Fnn exceeds 30 kV/cm. Field strengths far above 30 kV/cm, where the "plasma delay" should decrease linearly with the reciprocal field strength, were not attainable due to microplasma breakdown or charge multiplication, i.e. the linear extrapolation of To to infinite field strength (1/F = 0) appears to be questionable. In one case we observed at very high field strengths (28 < F < 45 kV/cm) an opposite slope of To (F) (decreasing To with increasing F). As a rule the "plasma-delay" time increases with increasing ion mass M (Z2 normally grows faster than M) and appears to be inversely proportional to the ion energy . 5. Discussion Our results clearly show that there is a dependence of the "plasma delay" on the detector properties such as resistivity, crystal thickness and area or, respectively, capacitance. Therefore it is difficult to compare our results with formulae for the "plasma delay" obtained by other authors [1,2] who could not extract a dependence on the detector properties due to the experimental technique used. Eearly measurements of the collection time or plasma-time (see e.g. ref. [7]), however, show qualitatively a p dependence of these quantities in accordance with our findings (eq. (3)). It should be stressed that the empirical formulae derived from our measurements contain an energy dependence quite different from the one obtained in earlier experiments . Neidel and Henschel predict that the "plasma delay" should be proportional to Et /z (see eq. (5) in ref. [2]), whereas we find as a rule a decreasing "plasma delay" with increasing energy. Only in a restricted energy range of very slow and heavy ions, Zz outweighs the energy term in eq. (3) with increasing energy, resulting in an increase of Td with the energy . Furthermore, the expression for F n obtained by Neidel et al. [1,2] is quite different from ours. For instance, in the case of 480 MeV °°Ar, their formula predicts a value of 138 kV/cm for Fm, n in contrast to our experimental result (Fn = 5.6 kV/cm) . In region II a comparison with other experimental data is not possible, because until now no one else made the attempt to fit this low field region. Eq. (4) provides at least an estimate of the "plasma delay" in this region but should not be strained too much. Very slow and heavy ions show a remarkably strong increase of the rise time at low field strengths and this in turn may lead to an overcompensation of the "plasma delay" even if the ARC-timing method is used. In many cases, if the field strength in region II is not too low it is a good approximation to use the constant value obtained from eq. (3) at F=F,n,n for the entire

W. Bohne et al / Influence of plasma effects on timing properties

range. But in case of a negative value of the logarithmic term in eq . (4) it is absolutely necessary to use this formula, see e.g . the Xe curve in fig. 5. Although several authors [3,12] reported that there is no real delay at the onset of the timing signals obtained from ions of different masses, our experiments clearly support the well known fact that there exists a mass dependent time shift in the observed time-of-flight. A possible explanation to resolve this contradiction might be that an ion dependent pulse shape at small amplitudes affects the constant-fraction discriminator, as already proposed by Neidel et al . [1]. In the constant-fraction method the timing signal is derived from the linear part of the fast signal which is delayed for signals with a small curvature at small amplitudes, i.e . for heavier ions (see e.g . fig. 1 of ref. [1]) . Of course, this is only true if the trigger point lies on the linear part of the signal . This is the case for all ions examined as long as the trigger fractions are between 0.2 and 0.8 . (Only for very heavy and slow ions this value should perhaps be somewhat larger than 0.2 .) This explains why the use of different constant-fraction discriminators and also different trigger fractions [2] does not alter the results remarkably . Due to the complicated nature of the "plasma delay" we did not attempt to give a physical explanation of the extracted equations. At this stage eqs. (2)-(4) should be understood as a recipe to correct for the "plasma delay" in time-of-flight measurements . 6. Conclusions The present investigation exhibits a dependence of the "plasma delay" on detector properties . Apart from a variation of Td with the field strength a dependence on the resistivity, thickness and area and the capacitance, respectively, of the detector is observed . Two equations, linear in 1/F (the inverse effective field strength), give a good account of the "plasma delay" observed for various ions impinging on several surface-barrier detectors. The first is valid for field strengths above F, which is determined by the ion and its energy and by the resistivity and the slice thickness of the .detector. This part shows the well known linear decrease with 1/F. Taking into account the detector properties this new equation is not as simple as the ones reported previously [1,2]. The second equation, describing the low field region, is even more complex. Nevertheless, with this set of equations it is possible to correct the time, velocity or mass spectra for different ions and energies obtained with constant-fraction dis-

criminators from surface-barrier detectors. Furthermore we can compare time-of-flight measurements done by different detectors. Additional measurements should be performed to confirm and/or improve the results. Though a convenient means, surface-barrier detectors are not well suited for accurate time-of-flight measurements. References [1] H.-O. Neidel, H. Henschel, H. Geissel and Y. Laichter, Nucl . Instr. and Meth. 212 (1983) 299 and references therein. [2] H.-O. Neidel and H. Henschel, Nucl . Instr. and Meth. 178 (1980) 137. [3] L. Hannappel, H. Henschel and R. Schmidt, Nucl . Instr. and Meth . 151 (1978) 537. [4] H. Henschel and R. Schmidt, Nucl. Instr. and Meth. 151 (1978) 529 and references therein. [5] M. Moszyhski and B. Bengtson, Nucl. Instr. and Meth . 91 (1971) 73 . [6] A. Alberigi Quaranta, A. Taroni, G. Zanarini, Nucl . Instr. and Meth . 72 (1969) 72 . [7] W. Seibt, K.E . Sundstr6m and P.A. Tove, Nucl . Instr. and Meth. 113 (1973) 317. [8] P.A . Tove and W. Seibt, Nucl . Instr. and Meth . 51 (1967) 261. [9] G.L . Miller, W.L. Brown, P.F . Donovan and I.M. Mackintosh IEEE Trans. Nucl. Sci. NS-7, No. 2/3 (1960) 185. [10] E.C . Finch, A.A . Cafolla and M. Asghar, Nucl . Instr. and Meth. 198 (1982) 547. [11] R.N . Williams and E.M. Lawson, Nucl . Instr. and Meth . 120 (1974) 261. [12] J. Girard, M. Bolore and J. Pouthas, Nucl . Instr. and Meth. 198 (1982) 557. [13] B. Martin, R. Michaelsen, R.C . Sethi and K. Ziegler, Nucl . Instr. and Meth. A238 (1985) 1 . [14] See for example Ortec, Application Notes AN 41 and AN 42 . [15] H. Meyer, IEEE Trans. Nucl . Sci. NS-13 (1966) 180. [16] C.A .J . Ammerlaan, R.F. Rumphorst and L.A .Ch. Koerts, Nucl. Instr. and Meth . 22 (1963) 189. [17] P.A . Tove and K. Falk, Nucl . Instr. and Meth . 12 (1961) 278. [18] P.A . Tove and K. Falk, Nucl. Instr. and Meth. 29 (1964) 66 . [19] N.J . Hansen, Progress in Nuclear Energy, vol. 4 (Pergamon, Oxford, 1964). [20] H. Henschel, H. Hipp, A. Kohnle and F. G6nnenwein, Nucl. Instr. and Meth . 125 (1975) 365. [21] L.C . Northcliffe and R.F. Schilling, Nucl. Data Tables A7 (1970) 233. [22] F. Hubert, A. Fleury, R. Bimbot and D. Gardes, Ann. Phys . Fr . 5 (1980) 1.