Full-energy peak efficiency of cadmium-telluride gamma-ray spectrometers

NUCLEAR

INSTRUMENTS

AND

METHODS

115 (1974) 13-2I; ©

NORTH-HOLLAND

PUBLISHING

CO.

FULL-ENERGY PEAK EFFICIENCY OF CADMIUM-TELLURIDE GAMMA-RAY S P E C T R O M E T E R S P. S I F F E R T , J P. G O N I D E C

a n d A. C O R N E T

Centre de Reeherches Nucldmres et Uniaersltd Lores Pasteur, Laboratmre de Phystque des Rayonnements et d'F~lectromque Nucldalre, 67037 Strasbourg Cedex, France R.O.

BELl

a n d t =.V. W A L D

Tyco Laboratorws, Waltham, Massachusetts 02154, U.S.A. Received 24 July 1973 T a k i n g m t o account the different interaction m e c h a n i s m s o f 7-rays with matter, we have calculated the pulse-height distrib u t i o n resulting from the b o m b a r d m e n t o f c a d m m m - t e l l u n d e (CdTe) counters by 1.3VCs a n d c o m p a r e d the results to the experimental d i s t n b u t m n s . C o m p a r i s o n s with equivalent s e n s m v e

v o l u m e S1(L0 and pure Ge counters have aiso been made. T h e dependence o f the full-energy peak etIlclency as a function o f applied bias voltage, p o s m o n o f the interaction, time relauve to the a p p h c a t i o n of bias, a n d energy of the incident radiation has also been investigated.

1. Introduction

itself and have established a tentative model for the process leading to the effectY). In counters prepared from indmm-doped CdTe, on the other hand, it has been observed that the area immediately under one contact is entirely lnactive8), necessitating geometrically asymmetric forward and reverse barriers for optimum performance. Thus, to assure that our results are not influenced by these factors, the in-

Recent progress in the quahty of cadmium-tellurlde crystals suitable for ),-ray detectors 1" 2) allows the possibility to determine experimentally the efficiency of these spectrometersa). Indeed, relative to earlier CdTe devices, present radiation-detection characteristics show so much less trapping-detrapping phenomena that an appreciable improvement in their energy resolution has been achieved. Therefore, to a first approximation, one may now state that the observed spectra result essentially from primary interaction of radiation with the cadmium-telluride medium. It then becomes possible to calculate the pulse-height spectrum r e s u l t i n ~ from ),-ray bombardment, as was done previously 6n germanium counters4). Taking into account the different modes of interaction ~of radiation," " we have calculated this distribution. The results have been compared with the experimentally observed distribution measured with a high-sensitivity, semi-insulating chlorine-doped counter, using 137Cs (662 keV) y-ray bombardment. Similar comparisons have been performed on nearly identical volume Si(Li) and pure Ge counters. Since it is recognized, however, that CdTe detectors still show certain types of peculiar behavior, a number of other evaluations were also performed. In particular, several people in addition to the present authors have observed a time dependent relaxation effect in detectors made from chlorine-doped CdTe s, 6). The effect has been evaluated in some detail by Malm and Martini 6) and by two of the present authors (R.O.B. and F.V.W.) who, with their co-workers, have shown that the magnitude of the effect is influenced by the metal used for the barriers as well as the material

13

Absorbed energy

Probab,M:,~

E

Cph(E)

I

B~cIT s )

E~h

J E - E°

( 1 - B )'q'c { TE ),B~c(TE')

E,,., -.- -, ,i, ,-,,,,, Fig. 1. Different possible interaction processes o f a p h o t o n of energy, E, with a detector.

14

v. S I F F E R T et al.

ferred to an electron, T, corresponds wholly to the ?-ray energy, E, a photoelectric interaction occurs, the cross section of which can be expressed by:

trinsic peak efficiency as a function of ?-ray energy, applied bias, and position of the interaction was investigated together with the behavior of the detector as a function of time. The results of these investigations are reported in section 6 of this paper, but it may be categorically stated here that none of the effects seem to influence in a substantial way the main results reported.

~rph(E) = A E - 712,

where A is a parameter depending on the absorption medium. When a Compton event occurs, resulting in a scattered photon of energy E', the transferred energy is only T~ = E - E L The cross section is expressed by Klein and Nishina 9) as:

2. Photon interaction in CdTe

For simplification, we will restrict our calculations here to rather low energy ?-rays ( < 2 MeV) in order to neglect pair productxon. Furthermore, we suppose that electron escape from the active volume is neghgible, although this hypothesis is not always completely valid in small counters (see discussion). The interaction of gamma radiatmn of energy E m a detector can occur through several processes which have been summarized in fig. 1. When the energy trans~'~

~rc(TE) = Do (nr~/a2mo c 2) (2 + [ T e / ( E -

Ts)] 2 x

T~)/E] -(2/~) (E- T~)/T~}),

x {1/~ 2 + [ ( E -

where ~ = E/(moe2), rn o is the rest mass of an electron, ro = e~ (too c2) is the classical electron radius, and Do is a constant that we assume equal to unity for simplification.

10

age

=:

CdTe

~Te

\, X\ \

t ~--k

Cd Te f

%

/

%%%%%

162

/~.I" /

~ % %% %%

~- photoelectric effect a" compton effect K~ pair creahon )J ,~. T.+ ~r+K

!

#

%%

10-3J

I

I1,1

~

I

I

I

I

I

I

i

t

I

1

i

i

r

i

i

t

E (MeV)

i

i

l

1o

Fig. 2. Linear absorption coefliclents o f Ge, Sl and CdTe as a function o f energy. Photoelectric, Compton, and pair-creation effects are shown.

CADMIUM-TELLURIDE

15

GAMMA-RAY SPECTROMETERS

Several possibilities exist for the scattered photon. They are: 1) To escape from the sensitive volume of the detector with a probability B~o(TE) , where B is the ratio of Compton scattered photons, P0, to the scattered photons, P. We assume that this ratio depends only on the detector and not on the energy of the impinging photons. 2) To be absorbed through a photoelectric process in the detector. The probability of this phenomena is given by:

at(re) (1 - B ) o'vh(E - TE). In this case all the energy is absorbed and results m a contribution to the "full-energy peak". 3) To be again scattered by a Compton event and to escape outside the sensitive volume. The probability of this phenomenon is given by: Go(T~) (1 -- B) c%(Te,)B.

Here, we restrict our investigation to the second effect, but we must take into account the 7-rays which are scattered by the medium surrounding the detector. Their energy hes between E and El (2c~+ 1). If C represents the fraction of the scattered )'-rays which enter the detector, the probability that a photon of energy E is captured by a photoelectric process is Caph(E), and that for a Compton process CB(rc(Te). The linear attenuation coefficients for the photoelectric, Compton, and pair-production interactions are shown in fig. 2 as a function of energy. The absorption (due to all processes) thicknesses as a function of energy are reported m fig. 3 for various attenuation values for both CdTe and Ge. The details of the computer program which uses these data for the calculation of 7-ray spectra have been published elsewhere4). 3. Experiments and results Due to the presence of the parameter C, indicating the influence of the external medium, all the measurements have been performed under the same external conditions, with lead shielding around the detector and source housing.

CdTe

[

, ' I AL

/ :.:.'.:::'

, " ' " ". .\ ,~_._.._.__z

]

V = 350 VOLts

°-.AL

Au

surfac~

St(LI)

barrier

V = 700 VoLts \

LI d i f f u s e d

B + ImpLanted ~Ge ,~.--___.z, ~Li

V = 20 VoLts diffused

c (MQV)

ACTIVE VOLUME ~ 2 5 m m 3 Fig 3 Absorption length for a fixed percentage loss as a function of incoming p h o t o n energy

Fig. 4. Geometry o f CdTe, Si(L0 and Ge detectors on which measurements were made.

16

P. S I F F E R T et al.

3. l. DETECTORS The CdTe counter was prepared from semi-insulating, chlorine-doped T H M grown crystals with a thin (1 000 A) aluminium contact deposited on lapped surfaces. The germanium detector was prepared from ultra-high purity material by implanting the rectifying contact. The silicon counter was lithium compensated and had a gold (200 A) surface barrier structure. Their sizes are given in fig. 4. The CdTe diode was operated at room temperature and the others at 77K.

lated spectra (figs. 5-7) was achieved with the values of the parameters as listed in table 1. An analysis of these data allows an evaluation of the behavior of the three detectors as compared to the theory. 4.2. EVALUATION OF THE PURE PHOTOELECTRIC EVENTS

Since parameter A is only a function of the photo100

3.2.

After recording the 7-ray pulse-height distribution for each detector with t37Cs, the spectra were simulated using a computer in the same manner as indicated in ref. 4. The results are reported for all three detectors in fig. 5-7. It appears that for energies above 150 keV, good agreement between the experimental and calculated spectra is obtained for the Si(Li) and Ge counters. In the case of CdTe, although satisfactory agreement exists, a tail appears on the low side of the experimental full-energy peak (see discussion below)

°70

'° 10

x~

0

701.-\

!,,/ caL'cuLoted

I

200

100

30O

~0 1300 CHANNELNUMBER

l°°]x,oo

l=3°

~ 7o

"

60

Ge DIODE

...

~60

k,V

•

:.

It.

~

Fig. 6. Pulse-height spectrum o f SI(L1) detector for la7Cs.

!

o

137Cssource _

4.1. DETERMINATION OF PARAMETERS A, B, AND C As indicated before, parameter A depends on the nature of the detector material, its volume and the geometry. For similar volume counters used under identical conditions, A is a function only of the photoelectric absorption cross section. In the same manner, B ]s a function of the Compton interaction probabihty. The best agreement between experimental and ca lcu.f :'..

SI(L,) dlode

"

m~ 60z~50

2O

[xloo

0.662HeV

O3

4. Analysis of the results

100

:x25

90K 5oo".

SPECTRA

-.:..

- -

-

20

CdTe diode 137Cs source

0.662MeV

-

137Cs source

0.662 MeV

%.~=e~.per,mental. ~

30 F

• f~,

""~: ex~nmentat 20

~""':':" ~'~

caLcut

IOO

200

300

tOO 500 CHANNEL NUMBER

Fig. 5. Pulse-height spectrum o f Ge detector for 137Cs.

0 ~

100

L_

200

3"~"-'~ - - 400': CHANNELNUMBER

Fig. 7. Pulse-height spectrum o f CdTe detector for 187Cs.

CADMIUM-TELLURIDE

GAMMA-RAY

SPECTROMETERS

17

TABLE l

TABLE 3

Values o f the parameters A, B a n d C for which the best results were obtained

Calculated contributions to the "photoelectric" peak due to photoelectric events a n d multiple C o m p t o n scattered events for the varmus counters.

A

CdTe Ge SffLl)

1-B

5.617 0.9675 0.07632

C

0.2108 x 10-~ 0.1488 x 10-z 0.1029 x 10-~

of

calculated

Calculated ratio o f p h o t o e l e c m c cross sections Experimental ratio o f A ' s

and

Muluple scattering into the full energy peak

(%)

(%)

51 61 71

49 39 29

0.3965 x 10-2 0.9125 x 10-2 0.3384 x 10-2 CdTe Ge Sl

TABLE 2

Comparison

Photoelectric counts

experimental

ratlos

o f A.

CdTe/Ge

Ge/Sx

CdTe/S1

5.3

12.0

62.5

5.8

12.8

75.0

exists between calculated and measured values. The small deviations can result from differences either in active volume or in geometry. 4.3. ANALYSIS OF THE EVENTS FALLING IN THE FULL-ENERGY PEAK

The "photoelectric" peak consists of two kinds of counts: those resulting from direct photoelectric events and those from multiple Compton scattered events Icaptured by a photoelectric process after multiple Compton scattering). If we assume that the full-energy peak has

electric cross section of the material, we can verify that the ratio found for the different media is in agreement with the calculated values (table 2). As can be seen in table 2, quite satisfactory agreement

/ o_

i

/

102

0,01

0.I

I

10

100

TIME CONSTANT (,us)

Fig. 8. Detector re~olution as a function o f the amphfier time constant for dxfferent leakage currents for CdTe.

18

P. S I F F E R T

a Gaussian distribution of the same area as the experimental peak, we can calculate the results listed in table 3. It appears that in the case of CdTe, almost half of all events in the full-energy peak result from multiple ill. teraction and not from direct photoelectric processes. 5. Discussion

As indicated before, the comparison between the calculated and experimental spectra leads to very good agreement in the case of Si(Li) and Ge counters, showing that the analytical method is accurate. In the case of CdTe the full-energy peak has a tad on the lowenergy slde of the experimental spectrum. This is not a result of the analytical method but originates from phenomena inherent in the device, such as trapping and detrapping m the material, inhomogeneitles, electron and X-ray escape, or polarization. Due to the small active volume and the rather high energy of the Cd and Te X-rays, the escape is also no longer negligible and contributes to the tail~°). Furthermore, charge collec106

1C 10 "~ lO

et al.

tion in state-of-the-art CdTe is not complete due to the presence of deep trapping levels in the bandgap. To obtain the o p u m u m energy resolution, rather short time constants m the amphfier have to be used, due to the leakage current (2 x 10-SA) of the detector at room temperature (fig. 8). As a consequence, carriers trapped on deep levels cannot be collected (fig. 9) since the longest possible time constants are necessary for full collection A compromise is therefore necessary. Cooling current quality materials does not improve the performance due to a very rapid increase of the detrapping time. Inhomogeneities probably play an unimportant role here as the scanning experiments reported below demonstrate. The role of polarization will also be considered below. 6. Full-energy peak efficiency of the CdTe detector as a function of several parameters 6.1. INFLUENCEOF THE BIAS VOLTAGE We have summarized m fig. 10 both the full energy and total efficiencles as a function of applied voltage, the impinging energy, and the side of irradiation. The results reported here correspond to spectra recorded shortly (1 min) after the voltage has been applied. It appears that a strong influence of the applied voltage exists. I f we compare the results of front and back side bombardment, we observe a large difference in efficiency, increasing with I'ower energies. Even if the back contact is much larger in size, the efficiency on this side is still much lower.

13-

<

E

6.2.

15

Scanning the detector with a collimated beam of 57Co over the front and back has shown at every point an identical pulse height for the photoelectric counts. Furthermore, no irregularities in the counting rate appear, but we observe that the back contact is active only over the same diameter as the front contact (fig. l l).

16 16 16 ~6

6.3.

lOld

16 lO-

S C A N N I N G T H E DETEC1-OR A R E A

5

15

25

35

45

55

65x10-2

Ec - E t ( = V )

F i g 9. T i m e t o d e t r a p a c a r e e r f r o m a level l o c a t e d E e - E t d e e p , f o r v a r i o u s t e m p e r a t u r e s . A c r o s s s e c t i o n o f 10 -15 c m 2 was assumed.

I N F L U E N C E OF TIME

We have determined the efficiency of the detector when irradiated by 57Co as a function of time by measuring the number of counts above the low-energy noise threshold per unit time (fig. 12). It appears that the counting rate decreases continuously with a time constant which, for this detector at 300K, is about 28 h. Switching off the applied voltage restores the original efficiency, but with a recovery Ume constant of about 0.5 ram. This result, which is similar to that observed several years ago in crystal counters t t), is due to polar-

CADMIUM-TELLURIDE

GAMMA-RAY

19

SPECTROMETERS

m

@

3 .o

o

57Co rat ro (D

@

uJ

fuLL energy peok

LL

2

•

/

__---

.....

,-~ ....

-7

~

1

08

I 100

I 200

I 300

I /~0 BfAS

500 VOLTAGE

(VoL~s)

Fig. 10. T h e efliclency for aTCo as a function o f applied bias for the C d T e detector. Both the total and the full-energy peak efficlencles are s h o w n for lrradlatxon f r o m either side o f the detector.

Dm,dG CdTe TYC:O Sconnmg 6 mm o290V

Diode CdTe TYCO Scanmng ~ 57Co 200 V

4~

2 ' D1

1,5 OJ

//

'

\\

5 10'

I

P0SITtON (ram)

-2

-1

I

I

0

+1

+"2 POSITION (ram)

Fig. 11. Scan o f the CdTe detector with a collimated 57Co source over t h e front a n d back surfaces o f the detector.

20

P. S I F F E R T et al

31(/ U3 I-Z 0

EFFICIENCY

vs

(polorzsotmn

onci d t p o t a r , s a t m n

TIME,

effects)

2~

•

=

t x = ~O"

,

105

104

I~

t B i o s sw,tched off I I , R i i , , i 1200 2ta3

2/.,00 TIME {s)

Fig. 12. The c o u n t i n g rate as a function of time with a 57Co source. The time scale is e x p a n d e d by a factor of 30 after the bias was removed.

RELATIVE EFFICIENCY CdTe - Ge

a~ w_

~o9 m

uJ -1-

LL LU

uJ

Sources • 207B, 570 keY (100) 106/, " (77} 1770 " (9) 131i 36/, ~ (100)

I~J > 0

t

I

I

100

200

300

I

tOO

I

r

500

BIAS VOLTAGE(VoLts)

•~ lo-1

LU IZ

638 m

(11,3)

60Co 1173 ~ (100) 1333 " (100)

V external 500VoLts

CdTe ~os Ld

=, 0.. I

0

G

50

,do

"

TIHE (ram)

10-3 0 O

> t,l~ ~

VoLts

>__

I

I

I

I

i

a I|l

I

1

I

I

l

I

I I o

l0 ENERGY (HeY)

Fig. 14. The relative efficiency of C dTe a nd Ge as a function of the p h o t o n energy.

UJ

,do

-

T IHE (mirE)

Fig. 13. The pulse he i ght as a ftmctlon of a p p h e d bias at zero t i me a nd as a functton of t i me is s h o w n by the top two curves. The derived effective voltage is s h o w n m the b o t t o m curve.

CADMIUM-TELLURIDE GAMMA-RAY SPECTROMETERS

21

lzation. But here, contrary to previous observations in other detectors, the source of the charge trapped on the deep levels which reduces the effective electric field in the detector is from thermally generated carriers, and not from charges generated by the incident 7-rays. Comparing the initial pulse height as a function of applied voltage (fig. 13) to the evolution of this pulse amplitude as a function of time, allows us to determine the mean effective field existing in the detector as a function of time. Further studies are necessary to better understand the origin of this polarization effect.

pared with the predicted values. Problems still exist, especially related to polarization effects, and a better understanding of the compensation of CdTe by chlorine and the preparation of purer material therefore seems imperative for further improvement of CdTe detectors.

6.4. INFLUENCEOF V-gAY ENERGY

References

The relative full-energy peak efficiency has been determined as a function of the impinging 7-ray energy by using several well known sources (2°7Bi, lalI, 6°Co) and it has been compared to that of an approximately equivalent sensitive volume intrinsic germanium counter. The results are reported in fig. 14. The slope of the curve (log-log plot) is very close to that of the change of photoelectric effect (fig. 2) with energy.

1) K. Zamo, W. Akutagawa and H. Montano, IEEE Trans. Nucl. Sci. NS-19 no. 3 (1972) 257. z) F. V. Wald and R. O. Bell, Nature, Phys. Scl. 237 (1972) 13. 3) H. L. Malm, T. W. Raudorf, M. Martam and K. R. Zamo, IEEE Trans. Nucl. Scl. NS-20 no. 1 (1973) 500. 4) j. p. Gonldec, G. Walter and A. Coche, Nucl. Instr. and Meth. 53 (1967) 185. 5) j. Palms, private communication 6) H. L. Malm and M. Martini, private communication. 7) R. O. Bell, G. Entree, and H. Serreze, accepted for publication in Nucl. Instr. and Meth. 8) W. Akutagawa quoted in ref. 3 see also ref. 3, p. 505. 9) R. D. Evans, Gamma rays, American Instztute o f Physics handbook, 2nd ed., Ed. D. E. Gray (McGraw HIll Book Co., New York, 1963) Ch. 8f, p. 8. 10) A. Cornet, P. Slffert and B. Schaub, dourndes d'l~tudes sut la spectrometric gamma (Grenoble, 1973). 11) K. G. McKay, Phys. Rev. 74 (1948) 1606, id. 77 (1950) 816.

l

7. Conclusion The results of the experiments reported here show that the improvements in the detector performance are sufficient to give a rather satisfactory agreement between the measured full energy peak efficiency as corn-

Two authors (R. O. B. and F. V. W.) wish to acknowledge the support of their contribution by the Defense Advanced Research Projects Agency and the U.S. Atomic Energy Commission, Office of Isotopes Development.