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Collection time and equivalent circuit of surface barrier semiconductor detectors
NUCLEAR
INSTRUMENTS
AND
METHODS
35 (I965) 83-87;
©
NORTH-HOLLAND
PUBLISHING
CO.
C O L L E C T I O N T I M E AND E Q U I V A L E N T C I R C U I T OF SURFACE BARRIER S E M I C O N D U C T O R DETECTORS* G. F A B R I a n d V. S V E L T O
Laboratori C.I.S.E., Milano
Received 19 December 1964 The rise time of silicon surface barrier detector pulses was measured, when excited by ~-particles. Such a measurement made it possible to check both the collection time of charge carriers in the depletion region and the equivalent circuit of the detector. The measurements were made by comparing, at the output of a fast amplifying chain, the waveforms due respectively to ~-particles and to artificial pulses obtained by injec-
ting a calibrated charge (6(t)-current pulse) into the detector. The measured parameter T turns out to be equal to T= T+RBCo+ReCo; where z is the collection time, Co the depletion layer capacity, Rs the bulk resistance due to the undepleted material and Rc a series resistance. It was experimentally verified that T, according to the theory, is a linear function of V-~ where V is the detector bias.
1. Introduction
It is important to point out that the considered equivalent circuit is mainly useful for rise time calculations and does not take into account some observed current tails in #sec rangeS-a).
In this work both the problems of collection time measurement of semiconductor detectors and of the equivalent circuit has been dealt with. Rs
~I
CO
2. Measurement method The block scheme of the experimental set-up is shown in fig. 2. The semiconductor detector exposed to an Am TM e-particle source is connected to a transistorized fast amplifier through a vacuum tube cathode follower.
Cs o
Fig. 1. Equivalent circuit of a semiconductor detector.
t.W
Fig. 1 shows the assumed equivalent circuit1). In this circuit Co is the depletion layer capacitance given by: Co = eS/W, where e is the dielectric constant of silicon, S the detector surface and W the depletion layer width, that for n-type silicon is equal to: W = 5.3 x 10 -5 (pV) ~ cm (V is the applied reverse bias in volt and p the silicon resistivity in O. cm). R s and Cs take into account the undepleted bulk material; RsCs = p~ is the dielectric relaxation time. The resistance R~ is given by R~ = p ( l - W)/S where 1 is the thickness of the silicon slice. R c takes into account every series resistance. In a previous work 2) an expression for the induced charge in a semiconductor detector was obtained; by using that the induced current I(t), ref. 3,4) turns out to be:
l(t) = Q exP I," t/pe)
8~-I
+V
"~I --I °mplifier'E~w-]°scill°sc°pe [~"], , plotter. I,
Fig. 2. Block scheme of the electronic system. A step voltage generator injects through a standard condenser a current pulse Q 6(t) of variable amplitude at the input of the cathode follower. The output voltage waveform is recorded by a sampling oscilloscope coupled to a X - Y plotter. The input equivalent circuit is shown in fig. 3; C1 is the input stray capacitance and A(p) is the transfer function of the fast amplifier. Ia represents the current injected by the artificial pulser.
(1)
Rs
where Q is the charge generated by the ionizing event in the depletion region. This expression was deduced for short particle range compared with the depletion region width; moreover, the carrier mobility was assumed to be independent from the electric field. * Work supported by EURATOM under contract no. 135.64.5 ISPI.
Fig. 3. Equivalent circuit of the semiconductor detector and amplifier. 83
84
G. F A B R I A N D V. S V E L T O
We will give here the main results; more details are shown in the Appendix. Let us consider, at first, the case for R c = 0. If we indicate with U(p) and Ua(p) the Laplace transforms of the output voltage pulses corresponding respectively to I(p) and Ia(p) we have the following relation (A3): =
l~(p) (1 + PZsCo)U(p )
(2)
where z , = RdO + pp ). It has to be noted that eq. (2) is not affected by A(p) and C1, that is by the transfer function and input impedance of the amplifier. Taking I,(p)= 1 and assuming for the a-particle current pulse an exponential waveform of time constant z, that is I(p)= 1/(1 +pz) we get from (2):
U.(p) = (1 + pZ~Co) (1 + pz)U(p).
(3)
From this equation it easily follows that:
1 +pz Pe+RsC°. U~(p)- U(p) U(p) (z + RsCo) z + R~Co p = 1 + ppe
(4)
For short range particles from (1) z is equal to pc; from (4) in the time domain we can deduce:
f t { U~(t)- U(t) } dt = (pe+gsCo)U(t) = TV(t).
(5)
0
The difference between the areas of the two voltage pulses (artificial and a-particle) is proportional, for every t-value, to the amplitude of the a-voltage pulse
J
at the same t; the proportionality coefficient being
T = pe + RsCo. Since R s = p ( l - W)/S and Co = eS/W we have: RsCo = pe {(I/W) - 1 }
(6)
T = pel/W.
(7)
and
Because W is proportional to the square root of the applied bias, the relation T vs V -~r must be a straight line through the origin with a slope dependent on the resistivity of the starting material and on the total thickness of the detector. 3. Experimental measurements and results The measurements were made with surface barrier silicon detectors prepared at C.I.S.E.; the starting material having different resistivity (p=350; 1800, 21000 f2. cm), with a slice thickness l between 200 and 1000 # and a surface S of 25 mm 2. The artificial pulser (Tektronix 110 type) injected a charge through a small condenser, equal to that corresponding to the a-particle. The fast amplifier was of the type described by C. J. Rush 9) and was fed by a cathode follower3). The voltage pulses were displayed on a sampling oscilloscope (Tektronix 661) and recorded on a X - Y plotter (Moseley 2D-2AM). The waveforms Ua(t) and U(t) were successively plotted for different values of detector applied voltage. Typical waveforms are shown in fig. 4. The minimum value of detector bias was so chosen as to have always or-particle range short compared to the depletion layer width. Ua(t) and U(t), so obtained, were analyzed by a digital computer in order to select the correct zero time satisfying for every t-value eq. (5);
Fig. 4. Typical Ua(t) and U(t) waveforms.
COLLECTION
TIME
AND
20
15
~ I0 h-
1__ W
Fig. 5. T vs V-½ for two semiconductor detectors: 15A4: p=1500f2.cm, S=25mm2, I=600/~. 18A3: p=1800f2"cm, S=25mm2, I=400/~.
EQUIVALENT
CIRCUIT
85
as a result of this fitting the parameter T was determined. Figs. 5, 6, 7 show the T-values so obtained and the interpolating straight lines as a function of V -½ for detectors of different thicknesses and resistivities. In order to verify that the obtained results are independent from the transfer function A(p) of the used amplifier, a measurement was repeated by using a different type of fast amplifier (H. P. 460 AR); same results were obtained. Although the experimental points may be interpolated by a straight line through the origin as predicted by eq. (7), the slope proved larger than the calculated one. Such a discrepancy can be attributed to the series resistance Rc (see fig. 1). In the Appendix it is shown that in this case also the same relation (5) holds, provided T has the following value: r = ps
l
+ Ro
sS
(8)
and the fitting is performed on the flat region of U(t). F r o m eq. (8) it follows that a series resistance changes only the slope of the line T=f(V-½). To verify eq. (8) measurements putting a series resistance to the detector were performed. As an example, in fig. 8 results for a 1500 f2. cm detector are shown. The calculated slope was 45 nsec.~/V; the measured one was 56 nsec.~/V; Ro was 85 I2. By putting a series resistance R* = 210 f2 the measured slope (80 n s e c ' v / V ) was consistent with the expected value (83 nsec-~/V).
15£
I0C
I,.5(
1E
10
2'0
30
4£) X(I0-2M-~
Fig. 6. Same as fig. 5 for: 210 A2: p=21000f2-cm, S = 2 5 m m 2 ,
12
l=500/z.
,4
2 tn
C
5
10
15
20 x(1;-2 V-1/~)
v-
Fig. 8. T as a function of V-½ for the detector 15A4 with and without a series resistance R* = 210 .Q.
o
~
lb 1
1'5 × (lo-2v-~/2;
Fig. 7. Same as fig. 5 for: 3.5A5: p=350D-cm, S=25mm2,
1=200~.
Results of a further measurement with an O R T E C surface barrier detector of nominal resistivity of 5000 f2. cm are shown in fig. 9. The slope is consistent with the physical constants of the detector; in this case R c seems to be equal to zero.
86
G. F A B R I
AND
V. S V E L T O
where: 3C
Rs Z~ = Ro + - -
1 + pp8
On the other hand for the artificial pulse we have: 2O
Ua(p) = Ia(p)A(p )
1 + PCoZ~
(A2)
1 1 PC1 "PC° Zs + pCoo + PC1
ta E 110
So, from (A1) and (A2) we obtain:
U(p) = Ua(p) I(p) Ia(p) { 1 + pCoZ, }" 0
10
ORTEC:
2'0
1___ VV"
30 X(10-2 V-1/2) -
Fig. 9. Tvs V-½ for detector: p = 5000 ~2.cm, S = 25 mm2, l = 650/~.
4. Discussion The described measurements allow the confirmation of the equivalent circuit shown in fig. 1. Moreover they represent an experimental check of the value of the l+p
Ua - U _ P
U{x+R,Co+R,Co}
Many thanks are due to Prof. E. Gatti for helpful discussions and suggestions. Thanks are also due to P. Torri and G. Giannini for the help in assembling and testing the electronic system and to Dr. A. Ghirardi for computer calculations.
Appendix The equivalent circuit of the input circuit is shown in fig. 3. For the voltage pulse U(p) corresponding to the e-particle, that is I(p) we have:
V ( p ) - I(p)A(p) 1 1 PC°'pCt Zs + ~ o + ~
(A1)
1
By assuming the current injected by the pulser to be a normalized &function, it turns out that Ia(p)= 1; therefore, for short range particles, that is for exponential current pulse, I(p) = 1/(1 + pz). With these assumptions equation (A3) becomes:
Ua(p) = U(p) (1 + pCoZ~) (1 + pz)
(A4)
and putting in (A4) the expression for Z~, we obtain
pe'RcCo + x(pe + CoR~ + CoR~) + p2 pe'r" CoRe z + CoR~ + CoRe z + C o R ~+CoRc 1 + pp~
induced current due to the carrier drift in the space charge region of the semiconductor2'4). It has to be noted in figs. 5 and 7, that the experimental points corresponding to the high bias values do not fit a straight line; as a matter of fact, the average electric field in this case is higher than 104 V/cm so the hypothesis of the constant mobility of charge carriers, does not stand. As a conclusion it has to be pointed out that, though in the considered case the charge collection time is equal to pe, the rise time of the voltage pulse at the input of the amplifier is dependent on its input impedance; only for infinite input impedance we get the value corresponding to collection time.
(A3)
(AS)
Let us consider, as a first case, Rc = 0; eq. (AS) becomes : 1 +pz
Ua - U _ U(z + RsCo) p
p8 + CoRs
z + CoRs . (A6) 1 + pp~
Now taking into account T = pc: Va - U = U { p e + R~C o }
(A7)
P from which we obtain, in the time domain, eq. (5). For Re # 0 eq. (A5) can be interpreted a follows: the area difference between Ua(t) and U(t) is proportional to the waveform U(t) filtered through a circuit characterized by the transfer function appearing in the second member ofeq. (A5). Since such a transfer function is of low-pass type, it does not affect for large t the quasi-step U(t) function. The ratio {Sto(Ua - U)dt}/U(t) performed for tvalues corresponding to the flat portion of U(t) gives, with a good approximation, the parameter
T = z + RsCo + R~Co.
(A8)
By expressing (A8) as a function of detector physical constants we have:
1
RosS
T = peV+-V-
COLLECTION TIME AND EQUIVALENT CIRCUIT It has to be n o t e d t h a t a series resistance R c affects only the slope o f the line T =
f(V-f).
References 1) F. J. Walter, Proc. Asbeville Conf., N.A.S.-N.R.C., Publ. 871 (1961) 237. 2) G. Cavalleri,G. Fabri, E. Gatti and V. Svelto, Nucl. Instr.and Methods 21 (1963) 177. 5) C. Cottini,E. Gatti,V. Svelto,P. Torri and F. Vaghi, Rapporto CISE, Euratom R 72 (1963).
87
4) C. Cottini, E. Gatti and V. Svelto, Instr. Techn. in Nucl. Pulse Anal., N.A.S.-N.R.C., publ. 1184 (1964) 53. 5) G. Fabri, E. Gatti and V. Svelto, Phys. Rev. 131 (1963) 134. G. Fabri, E. Gatti and V. Svelto, Instr. Techn. in Nucl. Pulse Anal., N.A.S.-N.R.C., publ. 1184 (1964) 49. 6) G. Bussolati, G. Fabri and A. Fiorentini, To be published on Phys. Rev. 7) F. S. Goulding, Instr. Techn. in Nucl. Pulse Anal., N.A.S.N.R.C., publ. 1184 (1964) 59. 8) E. Baldinger, I. Gutmann and G. Matile, Zeits. fOr Ang. Math. und Phys. 1 (1964) 90. 9) C. J. Rush, Rev. Sci. Instr. 35 (1964) 149.
INSTRUMENTS
AND
METHODS
35 (I965) 83-87;
©
NORTH-HOLLAND
PUBLISHING
CO.
C O L L E C T I O N T I M E AND E Q U I V A L E N T C I R C U I T OF SURFACE BARRIER S E M I C O N D U C T O R DETECTORS* G. F A B R I a n d V. S V E L T O
Laboratori C.I.S.E., Milano
Received 19 December 1964 The rise time of silicon surface barrier detector pulses was measured, when excited by ~-particles. Such a measurement made it possible to check both the collection time of charge carriers in the depletion region and the equivalent circuit of the detector. The measurements were made by comparing, at the output of a fast amplifying chain, the waveforms due respectively to ~-particles and to artificial pulses obtained by injec-
ting a calibrated charge (6(t)-current pulse) into the detector. The measured parameter T turns out to be equal to T= T+RBCo+ReCo; where z is the collection time, Co the depletion layer capacity, Rs the bulk resistance due to the undepleted material and Rc a series resistance. It was experimentally verified that T, according to the theory, is a linear function of V-~ where V is the detector bias.
1. Introduction
It is important to point out that the considered equivalent circuit is mainly useful for rise time calculations and does not take into account some observed current tails in #sec rangeS-a).
In this work both the problems of collection time measurement of semiconductor detectors and of the equivalent circuit has been dealt with. Rs
~I
CO
2. Measurement method The block scheme of the experimental set-up is shown in fig. 2. The semiconductor detector exposed to an Am TM e-particle source is connected to a transistorized fast amplifier through a vacuum tube cathode follower.
Cs o
Fig. 1. Equivalent circuit of a semiconductor detector.
t.W
Fig. 1 shows the assumed equivalent circuit1). In this circuit Co is the depletion layer capacitance given by: Co = eS/W, where e is the dielectric constant of silicon, S the detector surface and W the depletion layer width, that for n-type silicon is equal to: W = 5.3 x 10 -5 (pV) ~ cm (V is the applied reverse bias in volt and p the silicon resistivity in O. cm). R s and Cs take into account the undepleted bulk material; RsCs = p~ is the dielectric relaxation time. The resistance R~ is given by R~ = p ( l - W)/S where 1 is the thickness of the silicon slice. R c takes into account every series resistance. In a previous work 2) an expression for the induced charge in a semiconductor detector was obtained; by using that the induced current I(t), ref. 3,4) turns out to be:
l(t) = Q exP I," t/pe)
8~-I
+V
"~I --I °mplifier'E~w-]°scill°sc°pe [~"], , plotter. I,
Fig. 2. Block scheme of the electronic system. A step voltage generator injects through a standard condenser a current pulse Q 6(t) of variable amplitude at the input of the cathode follower. The output voltage waveform is recorded by a sampling oscilloscope coupled to a X - Y plotter. The input equivalent circuit is shown in fig. 3; C1 is the input stray capacitance and A(p) is the transfer function of the fast amplifier. Ia represents the current injected by the artificial pulser.
(1)
Rs
where Q is the charge generated by the ionizing event in the depletion region. This expression was deduced for short particle range compared with the depletion region width; moreover, the carrier mobility was assumed to be independent from the electric field. * Work supported by EURATOM under contract no. 135.64.5 ISPI.
Fig. 3. Equivalent circuit of the semiconductor detector and amplifier. 83
84
G. F A B R I A N D V. S V E L T O
We will give here the main results; more details are shown in the Appendix. Let us consider, at first, the case for R c = 0. If we indicate with U(p) and Ua(p) the Laplace transforms of the output voltage pulses corresponding respectively to I(p) and Ia(p) we have the following relation (A3): =
l~(p) (1 + PZsCo)U(p )
(2)
where z , = RdO + pp ). It has to be noted that eq. (2) is not affected by A(p) and C1, that is by the transfer function and input impedance of the amplifier. Taking I,(p)= 1 and assuming for the a-particle current pulse an exponential waveform of time constant z, that is I(p)= 1/(1 +pz) we get from (2):
U.(p) = (1 + pZ~Co) (1 + pz)U(p).
(3)
From this equation it easily follows that:
1 +pz Pe+RsC°. U~(p)- U(p) U(p) (z + RsCo) z + R~Co p = 1 + ppe
(4)
For short range particles from (1) z is equal to pc; from (4) in the time domain we can deduce:
f t { U~(t)- U(t) } dt = (pe+gsCo)U(t) = TV(t).
(5)
0
The difference between the areas of the two voltage pulses (artificial and a-particle) is proportional, for every t-value, to the amplitude of the a-voltage pulse
J
at the same t; the proportionality coefficient being
T = pe + RsCo. Since R s = p ( l - W)/S and Co = eS/W we have: RsCo = pe {(I/W) - 1 }
(6)
T = pel/W.
(7)
and
Because W is proportional to the square root of the applied bias, the relation T vs V -~r must be a straight line through the origin with a slope dependent on the resistivity of the starting material and on the total thickness of the detector. 3. Experimental measurements and results The measurements were made with surface barrier silicon detectors prepared at C.I.S.E.; the starting material having different resistivity (p=350; 1800, 21000 f2. cm), with a slice thickness l between 200 and 1000 # and a surface S of 25 mm 2. The artificial pulser (Tektronix 110 type) injected a charge through a small condenser, equal to that corresponding to the a-particle. The fast amplifier was of the type described by C. J. Rush 9) and was fed by a cathode follower3). The voltage pulses were displayed on a sampling oscilloscope (Tektronix 661) and recorded on a X - Y plotter (Moseley 2D-2AM). The waveforms Ua(t) and U(t) were successively plotted for different values of detector applied voltage. Typical waveforms are shown in fig. 4. The minimum value of detector bias was so chosen as to have always or-particle range short compared to the depletion layer width. Ua(t) and U(t), so obtained, were analyzed by a digital computer in order to select the correct zero time satisfying for every t-value eq. (5);
Fig. 4. Typical Ua(t) and U(t) waveforms.
COLLECTION
TIME
AND
20
15
~ I0 h-
1__ W
Fig. 5. T vs V-½ for two semiconductor detectors: 15A4: p=1500f2.cm, S=25mm2, I=600/~. 18A3: p=1800f2"cm, S=25mm2, I=400/~.
EQUIVALENT
CIRCUIT
85
as a result of this fitting the parameter T was determined. Figs. 5, 6, 7 show the T-values so obtained and the interpolating straight lines as a function of V -½ for detectors of different thicknesses and resistivities. In order to verify that the obtained results are independent from the transfer function A(p) of the used amplifier, a measurement was repeated by using a different type of fast amplifier (H. P. 460 AR); same results were obtained. Although the experimental points may be interpolated by a straight line through the origin as predicted by eq. (7), the slope proved larger than the calculated one. Such a discrepancy can be attributed to the series resistance Rc (see fig. 1). In the Appendix it is shown that in this case also the same relation (5) holds, provided T has the following value: r = ps
l
+ Ro
sS
(8)
and the fitting is performed on the flat region of U(t). F r o m eq. (8) it follows that a series resistance changes only the slope of the line T=f(V-½). To verify eq. (8) measurements putting a series resistance to the detector were performed. As an example, in fig. 8 results for a 1500 f2. cm detector are shown. The calculated slope was 45 nsec.~/V; the measured one was 56 nsec.~/V; Ro was 85 I2. By putting a series resistance R* = 210 f2 the measured slope (80 n s e c ' v / V ) was consistent with the expected value (83 nsec-~/V).
15£
I0C
I,.5(
1E
10
2'0
30
4£) X(I0-2M-~
Fig. 6. Same as fig. 5 for: 210 A2: p=21000f2-cm, S = 2 5 m m 2 ,
12
l=500/z.
,4
2 tn
C
5
10
15
20 x(1;-2 V-1/~)
v-
Fig. 8. T as a function of V-½ for the detector 15A4 with and without a series resistance R* = 210 .Q.
o
~
lb 1
1'5 × (lo-2v-~/2;
Fig. 7. Same as fig. 5 for: 3.5A5: p=350D-cm, S=25mm2,
1=200~.
Results of a further measurement with an O R T E C surface barrier detector of nominal resistivity of 5000 f2. cm are shown in fig. 9. The slope is consistent with the physical constants of the detector; in this case R c seems to be equal to zero.
86
G. F A B R I
AND
V. S V E L T O
where: 3C
Rs Z~ = Ro + - -
1 + pp8
On the other hand for the artificial pulse we have: 2O
Ua(p) = Ia(p)A(p )
1 + PCoZ~
(A2)
1 1 PC1 "PC° Zs + pCoo + PC1
ta E 110
So, from (A1) and (A2) we obtain:
U(p) = Ua(p) I(p) Ia(p) { 1 + pCoZ, }" 0
10
ORTEC:
2'0
1___ VV"
30 X(10-2 V-1/2) -
Fig. 9. Tvs V-½ for detector: p = 5000 ~2.cm, S = 25 mm2, l = 650/~.
4. Discussion The described measurements allow the confirmation of the equivalent circuit shown in fig. 1. Moreover they represent an experimental check of the value of the l+p
Ua - U _ P
U{x+R,Co+R,Co}
Many thanks are due to Prof. E. Gatti for helpful discussions and suggestions. Thanks are also due to P. Torri and G. Giannini for the help in assembling and testing the electronic system and to Dr. A. Ghirardi for computer calculations.
Appendix The equivalent circuit of the input circuit is shown in fig. 3. For the voltage pulse U(p) corresponding to the e-particle, that is I(p) we have:
V ( p ) - I(p)A(p) 1 1 PC°'pCt Zs + ~ o + ~
(A1)
1
By assuming the current injected by the pulser to be a normalized &function, it turns out that Ia(p)= 1; therefore, for short range particles, that is for exponential current pulse, I(p) = 1/(1 + pz). With these assumptions equation (A3) becomes:
Ua(p) = U(p) (1 + pCoZ~) (1 + pz)
(A4)
and putting in (A4) the expression for Z~, we obtain
pe'RcCo + x(pe + CoR~ + CoR~) + p2 pe'r" CoRe z + CoR~ + CoRe z + C o R ~+CoRc 1 + pp~
induced current due to the carrier drift in the space charge region of the semiconductor2'4). It has to be noted in figs. 5 and 7, that the experimental points corresponding to the high bias values do not fit a straight line; as a matter of fact, the average electric field in this case is higher than 104 V/cm so the hypothesis of the constant mobility of charge carriers, does not stand. As a conclusion it has to be pointed out that, though in the considered case the charge collection time is equal to pe, the rise time of the voltage pulse at the input of the amplifier is dependent on its input impedance; only for infinite input impedance we get the value corresponding to collection time.
(A3)
(AS)
Let us consider, as a first case, Rc = 0; eq. (AS) becomes : 1 +pz
Ua - U _ U(z + RsCo) p
p8 + CoRs
z + CoRs . (A6) 1 + pp~
Now taking into account T = pc: Va - U = U { p e + R~C o }
(A7)
P from which we obtain, in the time domain, eq. (5). For Re # 0 eq. (A5) can be interpreted a follows: the area difference between Ua(t) and U(t) is proportional to the waveform U(t) filtered through a circuit characterized by the transfer function appearing in the second member ofeq. (A5). Since such a transfer function is of low-pass type, it does not affect for large t the quasi-step U(t) function. The ratio {Sto(Ua - U)dt}/U(t) performed for tvalues corresponding to the flat portion of U(t) gives, with a good approximation, the parameter
T = z + RsCo + R~Co.
(A8)
By expressing (A8) as a function of detector physical constants we have:
1
RosS
T = peV+-V-
COLLECTION TIME AND EQUIVALENT CIRCUIT It has to be n o t e d t h a t a series resistance R c affects only the slope o f the line T =
f(V-f).
References 1) F. J. Walter, Proc. Asbeville Conf., N.A.S.-N.R.C., Publ. 871 (1961) 237. 2) G. Cavalleri,G. Fabri, E. Gatti and V. Svelto, Nucl. Instr.and Methods 21 (1963) 177. 5) C. Cottini,E. Gatti,V. Svelto,P. Torri and F. Vaghi, Rapporto CISE, Euratom R 72 (1963).
87
4) C. Cottini, E. Gatti and V. Svelto, Instr. Techn. in Nucl. Pulse Anal., N.A.S.-N.R.C., publ. 1184 (1964) 53. 5) G. Fabri, E. Gatti and V. Svelto, Phys. Rev. 131 (1963) 134. G. Fabri, E. Gatti and V. Svelto, Instr. Techn. in Nucl. Pulse Anal., N.A.S.-N.R.C., publ. 1184 (1964) 49. 6) G. Bussolati, G. Fabri and A. Fiorentini, To be published on Phys. Rev. 7) F. S. Goulding, Instr. Techn. in Nucl. Pulse Anal., N.A.S.N.R.C., publ. 1184 (1964) 59. 8) E. Baldinger, I. Gutmann and G. Matile, Zeits. fOr Ang. Math. und Phys. 1 (1964) 90. 9) C. J. Rush, Rev. Sci. Instr. 35 (1964) 149.