A risetime spectrometer for studying pulse shapes in Ge(Li) gamma-ray detectors

NUCLEAR

INSTRUMENTS

AND

A RISETIME

METHODS

64 (1968)

SPECTROMETER IN Ge(Li)

Chalk River Nuclear Laboratories,

0

NORTH-HOLLAND

FOR STUDYING

GAMMA-RAY

EIJI SAKAI*

Physics Division,

132-140;

PULSE

PUBLISHING

co.

SHAPES

DETECTORS

and T. A. McMATH

Atomic

Energy of Canada Limited,

Chalk River, Ontario,

Canada

Received IO May 1968

A risetime spectrometer has been developed to study the shape and distribution of shapes of y-ray pulses from Ge(Li) detectors. This instrument employs a time to amplitude converter, a multichannel pulse height analyzer, and two discriminators to measure the distribution of times required for full-energy y-ray pulses to reach a predetermined fraction of full pulse height. Using the

risetime spectrometer and collimated beam techniques, pulse shapes from a planar and a coaxial detector were determined as a function of the position of irradiation in the detector. The measured pulse shapes were in close agreement with calculated pulse shapes.

1. Introduction The excellent energy resolution of lithium drifted germanium detectors has led to their widespread use in the study of nuclear radiation. Large volume Ge(Li) detectors with high efficiencies are suitable for coincidence measurements. A knowledge of the shapes and distribution of shapes of the detector pulses is helpful in optimizing experiments, in particular in determining discriminator levels to minimize timing uncertainties or in the design of pulse shape selectors. Strauss, Larsen and Sifter’) have reported a study of the distribution of pulse shapes from planar Ge(Li) detectors; our measurements cover planar and coaxial detectors. If a series of distribution curves of the times required for y-ray pulses to reach predetermined fractions of their full pulse height is obtained, pulse shapes and pulse shape distributions may be derived; these also provide information on carrier mobilities and charge collection. The variation of pulse shapes and pulse shape distributions with position of ionization in the detector may be determined by using collimated y-ray beam sources’).

butions shown in the figures. The output pulses from the preamplifier are examined by a single channel pulse height analyzer, which gates the TAC signals to the multi-channel analyzer and ensures that only total absorption peak pulses are accepted. The components used in therisetime spectrometerare listed in appendix A; with the exceptions of the preamplifier and the low level limiter, these are commercially available units. The fast amplifiers have a risetime of 2 ns, adequate for the fastest output pulses from the preamplifier. The amplifier decay time is 5 ,us so that the risetimes of slow pulses are not modified; since decay time controls the baseline restoration at the input to the discriminators, it also places an upper limit on the count rate which can be used (in these experiments, count rates were less than 500/set). The discriminators are not pulse shape dependent. Fast pulser signals (less than 5 ns risetime) are fed into the preamplifier to measure the system risetime and monitor the system timing resolution. The TAC was calibrated by using a series of calibrated delay lines.

2. The risetime spectrometer

3. Experimental

The risetime spectrometer, shown schematically in fig. I, records the distribution of times required for full energy pulses to rise from a fixed low level (e.g. 6% of full pulse height) to a predetermined fraction of full pulse height, by means of a time to amplitude converter (TAC) and a multi-channel pulse height analyzer. The charge collected in the detector is integrated in a chargesensitive preamplifier. Start pulses to the TAC are taken from the output of the fast discriminator whose triggering level can be adjusted from IS:/, to 100% of full pulse height, and the stop pulses from the low level limiter after a 3.50 ns delay. This results in a reversed time scale (right to left) in the measured risetime distri-

Collimated y-ray beam techniques were used to measure the distributions of the shapes of pulses from a planar detector and a double-open-end (DOE) coaxial detector. The detectors used have excellent spectrometer characteristics; detector energy resolution for both detectors is 1.2 keV fwhm (E, = 662 keV) at z 1000 V/cm. The planar detector has a cross section of 3.8 cm2 and an i-region thickness of 0.9 cm. The coaxial detector is cylindrical, with a diameter of 2.6 cm and a length of 1.O cm. The p-core is 0.6 cm in diameter and the i-region is z 0.95 cm wide. Both detectors * NRC Energy

132

Postdoctoral Fellow, Research Institute.

on

leave

from

Japan

Atomic

PULSE

SHAPES

FROM

Ge(Li)

133

DETECTORS

1

SLIT COLLIMATED

13’Cs -

FAST LINEAR AMPLIFIER

-

LIMITER

-

DELAY GENERATOR

CLIPPING CABLE

tD

STOP START

-

HOLE

n+

COLLIMATED

SOURCE

FAST LINEAR AMPLIFIER

TIME

p+

TO

AMPLITUDE

-

_

CONVERTER (TAC)

FAST DISCRI MINATOR

LAYER

COAXIAL Ge (Li)

DETECTOR

Fig. I. A schematic diagram of the risetime spectrometer. The collimated y-ray beam sources used to irradiate different parts of the planar and coaxial detectors are shown.

were cleaned up in vacuum in the test cryostat until low leakage currents and flat capacitance-voltage curves were obtained. A narrow slit-collimated beam (slit 0.25 mm deep x 50 mm wide x 170 mm long) aimed parallel to the n+-i and i-p junctions was used to scan the planar detector in a direction perpendicular to the junction planes. The coaxial detector was scanned along a radius, using a beam collimated by a lead block with a hole 1 mm in diameter and 79 mm long aimed in a direction parallel to the detector axis. The arrangements are shown diagramatically in fig. 1. Pulse shape distributions were also obtained for uniform irradiation of the entire detector. For all measurements, a 137Cs source (E, = 662 keV) was used and the detectors were operated in vacuum at z 77°K.

produced. The shape of the pulse produced by a local interaction at a distance x0 from the n+-i junction may be expressed as

4. Planar detector

t, = t, when t 5 W( W-x,)/&l/);

4.1. CALCULATION

In an ideal planar detector, having a uniform electric field, and no noise or charge trapping effects, the shape of the detector pulse will depend both on the location of interaction and on the spatial distribution of charge

where n ,, = the number of electron-hole pairs produced, q = the electronic charge, t = the time after ionization; the terms t, and t, are limited by the times required for holes and electrons to travel to their respective junctions. If pe and p,, are the electron and hole mobilities respectively t, = t, when t 5 Wx,/&V); t, = Wx,/(~~li),

when

t, = W(W-x,,)/(p,V), T = the time required

width

W of the i-region T, = ~2/(U’),

t > Wx,/(peV);

when t > W(W--x,)/&V); for a carrier to travel the entire when voltage V is applied; Th = M/.2/(M’).

E. SAKAI

134

POSITION

OF

AND

IRRADIATION

Bz AB-

Q(t) be 0.5

v.3

T. A. MCMATH

in the distributions give the mean pulse shapes for these positions of irradiation. The risetimes from 0 to 0.9 V were 60 ns and 110 ns for irradiation at the centre and near the edge respectively, in approximate agreement with the factor of two difference predicted. The distributions obtained for irradiation at the centre showed tails towards slower risetimes, and those obtained for irradiation near the junction showed tails towards faster risetimes; these are due to multiple interaction pulses due to scattered y-rays. Fig. 5 shows the distributions obtained for uniform irradiation of the entire detector. The distributions for low discriminator levels show that most of the pulses have an initial fast rise, while the distributions near full pulse height show a shift toward slower risetimes. This is due to the two-component pulses resulting from interactions at positions between the centre and either junction, and to multiple interaction pulses.

1.0

TIME

(t/-f- 1

Fig. 2. Calculated pulse shapes for local interactions at different positions in an ideal planar detector. Uniform electric field, equal electron and hole mobilities, and negligible charge trapping have been assumed. Pulses corresponding to interactions near one of the junctions (B) take twice as long to reach full amplitude as pulses from interactions at the centre of the detector (A), because one of the charge carriers must travel the full width of the i-region.

Calculated pulse shapes are shown in fig. 2 for several positions of irradiation, assuming local interactions and under the simplifying assumption that electron and hole mobilities are equal [,uLe= ph = p, and hence T,= Th = T = W"/(,UV)]. Pulses from interactions near either junction take twice as long to reach full amplitude as pulses from interactions near the centre of the detector, since the contributing charge carriers must traverse the entire i-region. Interactions at intermediate locations produce pulses with two components: an initial fast rise, which lasts until one type of charge carrier reaches its junction, followed by a rise at half the initial rate to full amplitude, which is reached when the second type of charge carrier reaches the other junction. Multiple interaction pulses from scattered y-rays have more complicated shapes.

_

Ge(Li)

._

GlPl

_

500

_

COLLIMATED

MEASUREMENTS

Figs. 3 and 4 show the risetime distributions obtained with the collimated beam directed at the centre and near the i-p boundary respectively of the planar detector studied, with the discriminator level varied between 15% and 100% of full pulse height. The low level limiter was set at w 6% of full pulse height. The heavy lines drawn in to join the positions of the peaks

77”

v

INCIDENT

-

TIME

-

AT

(ns)

x 0.9cm) K ‘37Cs

SOURCE

THE

CENTRE

0.42ns/CH.

300 I,

0

4.2.

DETECTOR (3.Bcm2

/ I I I I, 200

I

I

I

400 CHANNEL

600 NUMBER

BOO

Fig. 3. Pulse risetime distributions obtained for y-ray interactions at the centre of a planar detector. The distribution curves should be regarded as standing perpendicular to the page; these represent the distributions in the times the full energy pulses took to reach different fractions of full amplitude. The heavy line joining the distribution peaks gives the most probable pulse shape for an interaction at this position. The tails on the distribution curves towards longer risetimes are due to pulses from multiple interactions from scattered v-rays. , .

PULSE

I”’

SHAPES

1’ ’ ’ I ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ I ’

FROM

(

PULSER

Ge(Li)

135

DETECTORS

more complex dependence on location of interaction, because of the non-uniform electric field (an r-l electric field dependence is assumed). In a conventional DOE coaxial detector having an outer n+ layer and a p-type core, electrons are accelerated outwards by a decreasing field, whereas holes are accelerated towards the core by an increasing field. For an interaction at a radius r,,, the pulse shape can be expressed as Q(r)l(n04)

= {2ln(rA~i))-‘. .[lnil

L I-. I L

-In

Ge (Li) DETECTOR GlPl (3.8 cm2 x 0.9 cm) 500 V 77°K

where r1 = the inner r 2 = the outer t = the time governed

COLLlMPlTED ‘37CSSOURCE INCIDENTIaT THE P - CONTAcT

radius radius after by the

+(tJT,)(ri-rT)!rZ> II

-(thlTh)(r:-r:)/r~}l,

of the i-region, of the i-region, ionization; the terms are again transit times of the carriers from

y-RAYS /

c-TIME

(ns)

0.42

__

ns/CH.

Fig. 4. Similar distribution curves to those shown in fig. 3 for interactions near the i-p junction. The tailson the curves towards faster risetimes are due to pulses from multiple interaction processes. Ge (Li)

The variation of risetime between 6% and 90% of full pulse height with the position of irradiation in the detector at three values of applied bias is shown in fig. 6. The points on the right hand side of fig. 7 show the mean risetimes, as derived from the peaks of the distributions in fig. 6, after subtracting the preamplifier risetime (35 ns) in quadrature. From these points, the velocities of the electrons and holes were derived; these are shown as a function of field on the left hand side of fig. 7. There is a distinct difference between these velocities (20% at 1000 V/cm), and neither has reached the limiting value (Z 1.l x 10’ cm/sec)3Y4) for this temperature. It is apparent that both the risetime and the spread of risetimes can be further reduced by the application of higher bias voltages. The three curves in the right hand portion of fig. 7 show the expected variations of risetime with location of interaction, as determined from the measured carrier velocities. 5. Coaxial detectors 5.1. CALCULATION The shapes of pulses from a coaxial detector

have a

DETECTOR

GlPl (3.8 cm2 x 0.9 cm) 500 V 77’K UNIFORM IRRADIATION 137Cs SOURCE

TIME

(ns)

0.42

ns/CH.

300 1,

0

,//,

i,‘,,‘,,‘,,‘,,‘,,,,,,,l,I 400 200 CHANNEL

PI’,

600

,‘,,“‘?l’,‘lO 600

NUMBER

Fig. 5. Pulse risetime distributions for uniform y-irradiation of the entire planar detector. The heavy dotted lines indicate the limits of pulse shapes resulting from all types of interactions producing full energy pulses. Most of the pulses have a fast initial rate of rise (sharply peaked distribution to 0.3 V), which lasts while both electrons and holes are moving to their respective junctions, followed by a component which rises more slowly to full amplitude (broad distribution at > 0.9 V), corresponding to the remaining movement of those carriers which have the longer distance to travel.

136

E.

Ge (LI)

DETECTOR

GlPl (38cm2

x 09 cm)

.,,..- .?.--SAKAI AND -1. A.’ MLMA L ” Sakai’), assuming single localized interactions and equal electron and hole mobilities. Pulse shapes calculated for five different positions of irradiation are shown in fig. 8. The difference in shape between the pulses for traversal of the entire i-region by holes (curve A) and electrons (curve E) is obvious; note, however, that, assuming equal mobilities, both pulses take the same time to reach full height. Pulses corresponding to irradiation at intermediate positions have components of both shapes, concave and convex upwards. The fastest rising pulses occur for ionization at

‘37Cs SOURCE DISCRIMINATOR BIAS IO V 77OK

5.2. MEASUREMENTS Risetime distributions were measured with the variable discriminator set at several levels between 15% and lOOo/o of full pulse height for five irradiation positions along a radius of the detector. The distributions obtained for irradiation near the junctions are shown in fig. 9, and mean pulse shapes for the five positions are shown in fig. 10. These curves are in good agreement with the pulse shapes calculated (fig. 8) for the

\‘. “NFORM

,RRADlATlON

1

I

Ij, I/

-, l’,;~;‘-,!‘I’I

0

t,

400 CHANNEL

‘I

I!1 1’1 1’1 ,’

600 NUMBER

800

f I’1 ,

DETECTOR GIPI DISCRIMINATOR BIAS 1.0 V 77°K

1

Fig. 6. Distributions of the times required for full energy y-ray pulses to reach 90% of full amplitude, as a function of the applied voltage and the position of irradiation in the detector. At the bottom of the figure distributions are shown for uniform irradiation of the detector at the same applied voltages. The difference in the distributions obtained for irradiation near the junctions indicates a difference in the electron and hole mobilities, rue > fit,.

the point where the ionization pective junctions: t, = t, for t s(ri

occurs to their res-

- rfJ [ln(r,/r,)]

t, = (4 - 4) C1n(r2/r1)] /(2~,k

CORRECTED FOR SYSTEM RISE TIME

/(l&1/); )?

for t>(r$-r~)[ln(r2/rl)]/(2peV); t, = t, for t r(r~-r:)[ln(r,/r,)]/(2/1,V); lh

=

(d-d) for

FIELD (v/cm)

t >

(r~-r:)Cln(r2/r1)]l(2~LhV);

T = the time required

for a carrier to traverse tire width (rZ - Y,) of the i-region :

the en-

T, = (~:-r:>[1n(r2/rl)l/(2~ev), Th = (r: Pulse shapes

TIME

(n;)

b(r2/rl)l/(2~hV)3

-I.:)[1n(rz/r,>l/(2~hV).

have been calculated

by Poenaru5)

and

Fig. 7. In the right hand portion of the figure, the points cofrespond to the observed mean risetimes, corrected for system risetime, plotted as a function of the position of interaction; the lines show the expected risetime variation with position for an ideal detector, calculated from the measured carrier velocities. The left hand portion of the figure shows the variation of carrier velocity with applied electric field; at the highest field used, neither carrier has reached its limiting velocity for this temperature.

PULSE

SHAPES

FROM

Ge(Li)

137

DETECTORS

Pn’Ye

r,/r,= 4.5

POSITION

OF

IONIZATION

--_(B) (C)

TIME

0.2

0

0.4

0.6

0.8

(t/T)

r,

r, =+kri)

+ r,

_

r, =+(r+J

+r,

_

-

1.0

Fig. 8. Calculated pulse shapes for local interactions at five different positions along a radius of an ideal double-open-end (DOE) coaxial detector. Equal electron and holemobilities,negligible charge trapping, and any-t variation of electric field were assumed in the calculation.

same r2/r1 ratio, with the possible exception of curve D. The 1000 V applied bias corresponds to a calculated minimum electric field of 560 V/cm at the outer radius of the sensitive volume, and a maximum field of 2340 V/cm near the core. Distributions obtained for uniform irradiation of the entire detector are shown in fig. Il. The relative number of fast-rising pulses is seen to be quite high. This is due to the finite low limiter level; pulses with slow initial I

I

I

I

rise appear shifted towards faster risetimes. Thus, pulses of types B, C, D and E are closer together at lower discriminator levels than in fig. 8, although their basic shapes are unchanged. Pulses of type A appear shifted by as much as 200/ of full transit time with the low limiter level set at 6% of full pulse height. Note that, from geometric considerations, a relatively large number of pulses should be of type A. This was less apparent in these particular measurements beI

Y-RAYS

I

1

I

PULSER

Ge(Li) DOE COAXIAL DETECT IOOOV 77°K COLLIMATED ‘=Cs Y-RAY

G22C4

INCIDENT

BEAM

0.8

NEAR

(A)

n*-i JUNCTION

(E)

i-p

-I Fz

JUNCTION

0.6

5

0.4

r E u-I

TIME

0

(ns)

0.385nsICH.

200

400

CHANNEL

600

600

1000

NUMBER

Fig. 9. Measured pulse risetime distributions for y-irradiation near the n+- I and i-p junctions in a DOE coaxial detector. Pulse shapes of type A, with slow initial rise, are prominent in coaxial detectors because a relatively large fraction of the sensitive volume lies in the outer, low field, regions.

138

E. SAKAI

AND T. A. MCMATH

Y-RAYS

G22C4

1000

COLLIMATED

V

77°K

‘“‘Cs Y-RAY

POSITIONS

PULSER

I.0

2 -I w

0.8

5

0.6

:

BEAM

( I mm DIA.COLLlMATOR

1

z z

TIME

(ns)

0.385

ns/CH.

0.4

5 n 0

0.2

g

0 200

0

400

600

800

1000

CHANNEL NUMBER Fig. 10. Mean pulse shapes derived for y-irradiation at five different radial positions in a DOE coaxial detector. These curves can be compared with the calculated shapes of the same letter designations shown in fig. 8. Because of the finite level of the lower discriminator (M 6% of full pulse height) the zero time point in the figure is actually not the same for all pulses. Those which rise slowly initially have in effect been shifted towards zero time.

cause the detector showed a much lower full energy peak efficiency in the outer parts of the i-region. This effect was not explainable from geometric considerations of the absorption of scattered y-rays, and was not present during an earlier series of measurements on the same detector; no change in energy resolution was observed. A similar effect has been observed in one I

I

other DOE coaxial detector, and is under investigation; it may be related to cleanup, or to the formation of an insensitive layer on the end face extending in from the periphery of the i-region. The measured risetime distributions for uniform irradiation were thus distorted because the relative number of slow rising pulses was reduced; however, these efficiency variations did not I

I

I

-

Ge(Li)

-

COAXIAL

I

I

Y-RAYS

I

PULSER

DOE DETECTOR

G22C4

77°K

~ _._

1.2

>

-~-

I.0

ti > W A

IOOOV -

UNIFORM “‘Cs

IRRADIATION Y-RAY

0.8 g

s

SOURCE

-

0.6

-

0.4

-

0.2

k z r

TIME

(ns)

I

300 I

I~l~l~l’l~l’l~lr~~~ll

0

200

0.385

ns/

I

CH.

I 400

CHANNEL

Fig. 11. Pulse risetime distributions

I

I

600

I

800

I

0

1000

NUMBER

for uniform y-irradiation

of the coaxial detector.

5 v, 6

PULSE SHAPES FROM Ge(Li) affect either the width of the time distribution pulse shape derived from collimated irradiation particular location in the detector.

or the at any

6. Discussion The most severe limitation to the accuracy of the method of measurement described is the one mentioned above - that the finite level of the low level limiter narrows the measured risetime distribution by shifting pulses with slow initial rates of rise towards apparent faster risetimes. Proportionately, this has a greater effect at low discriminator level settings; the effect is greater for coaxial than for planar detectors because of the larger variation in the initial rates of rise of the pulses. One way of eliminating this shift would be to scan with the 511 keV annihilation y-rays from a positron source located near the middle of a collimator open at both ends; the y-rays in coincidence with those directed into the Ge(Li) detector would be detected in a fast scintillator placed behind the collimator, and would provide time zero pulses to the TAC. Several other factors should be considered in interpreting these results. Multiple interactions were not taken into account in the calculations. Sharp corners in the pulse shapes were rounded by risetime limitations in the preamplifier used; a faster low-noise preamplifier would reduce this. The distribution measured at each location was broadened by the finite beam size, and by any slight misalignment of the beam with respect to the detector junction planes or core axis; to minimize this effect, a small area planar detector and a coaxial detector of short axial length were used. The pulse shape distribution measurements on the planar detector are complementary to those of Strauss et al.‘), who obtained distributions of the heights reached by pulses clipped at different times after interaction in the detector by varying the length of the clipping delay line. With their method, the time distribution very near full pulse height can be determined without encountering the problem of measuring a very broad distribution directly; it also avoids the problems associated with the low limiter level. The present method has the advantage of providing a direct determination of the spread in risetime at any fraction of full pulse height. The measurements obtained by the two methods are in good agreement. Using the risetime spectrometer, a direct measurement of the timing uncertainties for a given detector can be obtained, or conversely, the optimum size of detector can be selected for a given application. The spread in risetime at 50% of full pulse height and at low levels are of interest for zero cross over or leading

DETECTORS

139

edge timing. The reduced time spread at low levels is evident in both planar and coaxial detectors. Note that the distributions shown here were obtained from full energy pulses from a monoenergetic source, using fixed discriminator levels. Pulses of different heights will display different time distributions at a given discrimination level; thus a measurement obtained for y-rays of different energies, and including Compton scattered events, by the method described would not closely resemble the distributions shown above. However, if the discriminator triggered at a fixed fraction of the pulse amplitude, pulses of different amplitude should have the same time distribution, apart from some modification due to variation in scattering with E,. A constant fraction discriminator set at a low level should therefore give best results in timing circuits with Ge(Li) detectors. In applications where timing accuracy is essential and some loss in detection efficiency can be tolerated, a considerable improvement can be achieved very simply by partially collimating the radiation incident on the detector, i.e. by shielding those parts of the detector in which the pulses with the slowest initial rise originate. Thus a planar detector would be irradiated from the side, through a wide slit placed mid-way between the junctions. A coaxial detector would be irradiated from one end, through a ring concentric with the detector which would shield the outer junction. For example, a shielding ring which restricted interactions to locations nearer the centre than position B (fig. 8) would reduce the solid angle of the detector end by about one third, but would reduce the time spread by two thirds at 10% of full pulse height or by half at 50% of full pulse height. This approach would be most effective with detectors of short dimension along the direction of irradiation and placed far from the source. The authors gratefully acknowledge the continued support and encouragement of Mr. I. L. Fowler, and the technical assistance of Mr. W. F. Slater. Appendix A COMPONENTSUSED IN THE RISETIME SPECTROMETER Preamplifier - Chalk River design - one FET, operated at room temperature, Main linear amplifier - Tennelec TC 200, Single channel analyzer - Ortec Model 420, Linear gate - Ortec Model 409, Fast linear amplifiers - LeCroy Research Systems Model 133, Limiter - Chalk River design, Delay generator - Ortec Model 416,

140

E. SAKAI

AND T. A. MCMATH

Fast discriminator - Ortec Model 417, Time-to-amplitude converter - Ortec Model 437, Multi-channel analyzer - Digital Equipment Corporation PDP 8, with an Intertechnique CA 13 analogto-digital converter. References I) M. G. Strauss, R. N. Larsen and L. L. Sifter, IEEE Trans. NS-13, no. 3 (1966) 265.

2, P. P. Webb, H. L. Malm, M. G. Chartrand, R. M. Green, E. Sakai and I. L. Fowler, Nucl. Instr. and Meth. 63 (1968) 12.5. 3, E. Sakai, H. L. Maim and I. L. Fowler, presented at the Gatlinburg Conf. Semiconductor nuclear particle detectors and circuits (May 1967, Proc. in press) also AECL-2762. 4, D. M. Chang and J. G. Ruth, Appl. Phys. Letters 12 (1968) 111. 5, D. N. Poenaru, IEEE Trans. NS-14, no. 5 (1967) I. 6, E. Sakai, IEEE Trans. NS-15, no. 3 (1968) 310.