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Compensation of trapping losses in CdTe detectors
296
Materials &'ience and Engineering, B16( 1993': 296-3(} 1
Compensation of trapping losses in CdTe detectors M. Richter, P. Siffert and M. Hage-Ali Centre de Recherches Nucleaires (IN2P3)--Laboratoire PtOt~E ~(~)~'Rdu CNRS No. 292), BP 20, F-6 7037Strasbourg Cedex (France)
Abstract Energy resolution and photopeak efficiency of planar CdTe ttlt~lL~tf ~di~iiion spectrometers are degraded by charge trapping effects in the bulk of the detector. Chari~ 1o~ ~ g ~ t f i o n methods result in an enhancement of energy resolution and photopeak efficiency, but these t e c h n l q ~ O[b~tate only with certain detectors. In this article we present data from dual-parameter gamma-ray sp~trotll~l'y ~ad time-of-flight experiments to characterize these devices. A computer model of the charge collection inside the detector will be discussed.
1. Introduction Cadmium telluride (CdTe) is a material of interest as a highly sensitive, room temperature-ope~tin8 gamma-ray spectrometer. Modem detectors offer good stability and energy resolution. The best energy resolution up to now of about 0.5% at 662 keV has been achieved by using a slightly cooled detector with a p-i-n structure [1]. However, owing to the small electron and hole mobilities in the p-type material generally used, the sensitive region of these detectors is only 0.1-0.3 mm thick. Thus, detection efficiency is rather limited. In CdTe detectors having a metal-semiconductormetal (m-s-m) structure the depletion layer can be quite thick (about 1-2 mm). Therefore these devices are much more sensitive; however, the energy resolution and photopeak efficiency of such a thick planar CdTe detector are degraded owing to poor hole transport properties. Consequently, the field of application is still limited. Different approaches to detector geometry and pulse processing techniques have been tested to overcome these shortcomings [2, 3]. However, mostly they did not result in much better resolution or they caused severe problems with detector stability and efficiency loss. Charge loss correction methods are the most promising [4]. They are based on the assumption that poor energy resolution is mainly related to trapped holes, while the electrons are collected almost without any losses. Because of the much higher mobility of the electrons, the overall charge collection time is determined by the collection time of the holes. The relation between the energy loss fraction and the charge collection time has been measured experimentally and based 0921-5107/93/$6.00
on these data we could establish a correction function. This results in a tremendous improvement in energy resolution and photopeak efficiency. However, this correction method still demands devices made from nlat~rials with sufficiently high hole mobility. In this lyaper, we present some recent results performed some of these "good" detectors.
2. Dual-parameter spectrometry The goal of the experiment was to investigate the variation of the spectrum shape as a function of the charge collection time. Using the Charge Loss Correcter of the firm EURORAD [5], which provides for an optional second output of the risetime information in coincidence with the pulse height at the energy output, we measured dual-parameter spectra of different radiation sources with gamma-ray energies from 60 keV (241Am) up to 662 keV (137Cs). The spectra show clearly that the initial result can be regarded as a summation of subspectra with shifted photopeaks. The subspectrum near the shortest risetimes offers the best energy resolution and peak-toCompton ratio (Fig. 1). This matches the experience gained with resolution enhancement using risetime selection systems [3, 4]. Spectra measured with longer risetimes have worse resolution and spectrum shape. Unfortunately, this limits the performance of charge loss correction methods and demands a pulse preselection to suppress pulses with collection times that are too long. The application determines a compromise between efficiency and energy resolution [5]. The photopeak intensity of these subspectra decreases nearly exponentially with increasing charge © 1993 - Elsevier Sequoia. All rights reserved
M. Richter et al,
/
Compensating trapping losses in CdTe detectors
137-Cs spectra measured with different nseame windows
2~s
297
122keV m,
./k.__ ./k__
A
,t0oos 56
100
150
20o
25O
30O
35O
400
450
500
ehaaae.l number
Fig. 1. This dual parameter spectrum of a ~37Cssource demonstrates that the untreated energy spectrum measured with a CdTe detector can be regarded as a superposition of shifted subspectra resulting in the low energy tailing of the photopeaks. Each subspectrum is generated in a different layer of the detector.
Fig. 3. Dual parameter spectrum of a 57C0 source. Compared with the corresponding ~37Csspectrum of Fig. 2, the intensity of the photopeak decays faster. The constant of this exponential function corresponds well with the absorption coefficient.
662kcV
"-'t)O.7
Fig. 2. Dual parameter spectrum of a 137Cssource. The intensity of the 662 keV photopeak decays following the absorption
Fig. 4. Dual parameter spectrum of a 137Cs source. This point of view shows clearly the linearity between photopeak shift and charge collection time.
curve.
collection time (Figs. 2 and 3). The constant of this exponential function is approximately equal to the absorption coefficient of CdTe for this energy. The error can be explained by the influence of the inhomogenous electrical field inside the detector (see below). This indicates that the phonon energy is absorbed at one point. The relative charge loss depends only on the depth of the carrier generation and not on its initial number. T h e low energy tail of the photopeaks appears as a superposition of shifted subspectra with decaying intensity. As already mentioned formerly, the photopeak shift, i.e. the relative charge loss, is linearly proportional to the risetime a n d d o e s not depend on radiation energy (Figs. 4 and 5). Of course the question of why it is linear still remains.
3. Current pulse measurements To get some more information about the shape of the electrical field inside the detector we must follow the path of the carders from the point of generation to the contacts. One way to do this is to measure the current pulse. The current is proportional to the number of carriers and their speed. The speed is the product of mobility and electrical field. This means that for a constant number and mobility of carriers the current pulse I(t) gives directly the function E(t). If we arrange a way for the charge to be transported through the whole detector by exclusively one carrier type, then the current pulse I(t) is proportional to E(x). We can fulfil these conditions if we irradiate the negative-biased surface of a detector with alpha-parti-
298
,~t. Richter et aim
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7
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~_00021 ; 0
Fig. 5. Dual parameter spectrum of a 57Co source. It is shown that the linear peak shift does not depend on gamma-ray energy.
cles or soft X-rays. The charge will be transported by electrons to the positive contact. For a sufficiently high bias voltage the carrier transit time is small in comparison with its lifetime. Thus the shape of the electron current pulse is mainly influenced by the shape of the electrical field. In our experiments we used 2 mm thick CdTe detectors with platinum contacts. The bias voltage varied from 100 V to 300 V. The electron lifetime was measured to be at least 1 Its. A fast current-sensitive preamplifier in a closed loop configuration has been used for the measurements. A high open loop gain ensures short risetimes and accuracy. The results were rather unusual (Fig. 6). The electrical field has its maximum near the negative contact of the detector and decays more or less exponentially in the direction of the positive side. This is completely contradictory to former investigations of detector polarization [6, 7]. We repeated these experiments with many "good" detectors, that is, with devices which work well with the E U R O R A D Charge Loss Correctot. The results were always similar. Further, we observed also the hole current pulses (Fig. 7). Although the collection time of the generated charge is much longer, the current decays only slightly. For higher detector bias voltages the hole current is rising with time. Thus, the higher speed of the holes near the negative contact can obviously compensate for the number of carriers lost by trapping. This also means that the speed of the holes in all layers of the detector is still proportional to the electrical field. Another unexpected observation was the ratio of the currents of electrons to that of holes. A voltage pulse at the output of a commonly used charge-sensitive preamplifier represents the integral over the detector current pulse. If we compare the slopes of the fast and slow fractions of such a pulse we get a ratio of about 6
...................
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6
7
8
9
10 x l 0 "7
Fig. 6. Current response from alpha-particle irradiation of the negative detector contact. The electron current pulse decays much faster as we would expect from the carrier lifetime. Even for a shorter collection time (see lower curve) the pulse shape does not change substantially. This phenomenon can be explained by a non-homogenous electrical field inside the detector.
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7
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Fig. 7. Hole current pulse after charge generation at the positive detector contact. Although the holes move much slower than the electrons we do not observe a current decay. The electrical field obviously accelerates the holes in the direction of the negative
contact and compensates in such a way for the number of cartiers lost by trapping. This does not mean that the hole collection efficiency becomes better, as it depends only on the final collection time, but it proves that the electrical field increases against the negative contact.
to 12. For the penetrating 662 keV radiation of a ~37Cs source we got similar results using the current amplifier (Fig. 8). In experiments with alpha particles we measured an electron current 50 times higher than that of holes. This indicates the existence of a dead layer near the positive contact. Thus, only a small fraction of the
M. Richter et al. SS-2A Vdet
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Compensating trapping losses in CdTe detectors xl05
= 125V
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Fig. 8. The detector was irradiated with a ~37Cs source. The current pulse demonstrates the ratio of electron and hole current at a point in the middle of the detector.
generated carriers reaches the internal collection field and the hole current is much smaller. T h e main result of the current measurements was the discovery of the fast polarization of the used detectors. T h e electrical field has its maximum at the negative contact and is decaying exponentially. This results in faster hole collection and in some unusual current pulse shapes.
4. Modelling As a result of these calculations we expected a better understanding of the influence of the different detector parameters on the charge collection efficiency. T h e basis of our detector model comes from the observation of the current pulses. By varying the model carrier properties, such as mobility and lifetime, and also the field distribution, we fitted the calculated curves to the actual measured pulses. T h e final model matches well our experiences of real detectors, in which we have: Electrons: Un = 1 100 cm 2 V- 1 s- 1 _- constant rn = 1 ~S Holes:
up0 = 80 cm 2 V - 1 s- 1 up(x) = f ( E ) = up0 + h * E ( x ) r p - - 1 ~s
Field:
E = E 0 * exp( - k* x)
Detector:
thickness d = 1.9 m m negative contact: x = 0
With constant hole mobility and a realistic lifetime it was not possible to reconstruct the observed pulse shapes. Oltaviani et al. [6] found a relation between the electrical field and the hole mobility (Poole-Frenkel
0I
0
1
2
3 C011eCtlOtl lime {s]
4
5 x l 0 "7
Fig. 9. Electron current pulses in(t) of the model detector calculated for different values of the electrical field at the negative contact. These correspond to detector voltages of 100 V, 200 V and 300 V, for i = 1, 2 and 3 respectively. The resulting curve is the superposition of trapping loss and the decay of carrier speed. effect). In the case of a high electrical field inside a biased detector this relation can be linearized. To display the current pulse we have to calculate the speed and n u m b e r of carriers in the time period tcon between the generation of charge at the point x 0 and its recombination at the contacts. T h e fraction of the carriers reaching the contacts is determined only by the collection time. n = n0* exp( - tcon/r)
(1)
Assuming the proportionality of speed and electrical field we can write for the electrons: v(t, x0)=
1 t*k + 1/V(Xo)
(2)
For the holes the integrals are more complicated owing to the non-constant mobility. We solved the equations numerically. Figures 9 - 1 1 present current pulses for different values of the electrical field generated at different positions inside the detector. T h e current pulses for x = 0 and x = d corresponds to the experiments with alpha particles. T h e electron current is a good match to the real data. T h e main difference is the presence of noise and the limited bandwidth of the current amplifier used for the measurements. T h e important discrepancy for the holes can be explained by the existence of a thin dead layer under the positive contact which has been neglected in the calculation. We were more interested in the principal pulse shape. For charge generation in the middle of the detector (Figs. 8 and 11) the model is in agreement with the experimental data.
300
:14. Richter et al. xl05
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('ompensating trapping losses in CdTe detectors
un=ll00up=80 d---O.19 xo=O.19 k=5 h=0.002
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: 2ip(t)
---
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0I
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4
collectiontame [s]
xlO "6
Fig. 10. Calculated hole current pulses/p(t). Near the negative contact the holes are moving faster.The number of carriers lost by trapping can be compensated. For higher electricalfields this effectis more impressivc.
xl05
un=ll00 up=80 d=0.19 xo~0.1 k=5 h~0.002
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-, . . . . . . . . .
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Fig. 11. For this calculation a charge generation in the middle of the detector has been assumed. Both carder types take part in the charge collection (electron current: solid line; hole current: dashed line).
The resulting curves of collected charge vs. collection time of the adapted detector model are presented in Fig. 12. They tend to be linear. The value of the applied electrical field changes only the gradients of the curves, but not their fundamental shape.
5. Discussion
The investigated detectors have followed the evolution of technology since 1983. They are made from highly resistive material which has been grown in a
015
i
~;
i
2;
3
charge coll~tion tame Is]
3;
i
;.5 xl0 "6
Fig. 12. The function of the collected charge vs. collection time of the modelled detector tends to be linear.
travelling heater method (THM) process under Te pressure. As contact material platinum or gold is used. The sensitive surface area is between 25 mm and 56 mm 2. The devices are mostly 2 mm thick. The best energy resolution can be achieved if the negative side of the detectors is irradiated. With current pulse measurements it was found that the electrical field inside the detectors has its maximum at the negative contact. Because we still obtained a signal from alpha-particle irradiation of the positive side we think that the "dead layer" there is very thin. This is totally contradictory to former investigations [7]. Only for an old detector made from n-type material with Al contacts did we observe the same direction of polarization. The T H M material is normally suspected to be p-type but experimental confirmation is rather difficult owing to its high resistivity. The influence of contact material is not so clear yet. For detectors from one CdTe ingot the orientation of polarization changes if we contact them with gold instead of platinum; for another ingot the detectors polarize independently of the contact material in the "wrong" direction. Analysis methods such as thermal scanning calorimetry or secondary ion mass spectrometry did not offer suspicious differences. Furthermore, we could not measure a change in the detection efficiency vs. time. So we assume that the polarization is a very fast process. Up to now we are unable t o explain these phenomena. Although nearly all newer detectors show this inverted polarization, only a small number of them provide good results with the linear charge loss correction method. As also proved by the model, only detectors with a sufficiently high mobility-lifetime product for holes work well.
M. Richter et al.
/
Compensating trapping losses in CdTe detectors
301
To select detectors for the correction, we irradiated them with the deeply penetrating 662 keV gamma rays of a 137Cs source. We observed the output pulses of a normal charge-sensitive preamplifier. If they are composed of slow and fast rising fractions it is probable that this detector works well with our charge loss correction circuit.
on the charge collection efficiency has been investigated. The function of relative charge loss vs. charge collection time of this model detector is nearly linear and correlates well with experimental data. The observation of fast polarization in CdTe detectors made from highly resistive p-type material is still incomprehensible.
6. Conclusion
References
By means of dual-parameter spectroscopy the function of relative charge loss vs. collection time was measured. The experiments demonstrated once more the linearity, and independence of photon energy, of relative charge loss. With time-of-flight measurements it has been discovered that the electrical field inside some "good" detectors is exponentially shaped. By means of a computer model the influence of this field distribution
1 A. Kh. Khusainov, Nucl. Instrum. Methods, in press. 2 K. Zanio, Rev. Phys. Appl., 12(1977) 343. 3 U. Hagemann, R. Berndt and R. Arlt, Kernenergie, 31 (1988) 54. 4 M. Richter and P. Siffert, Nucl. Instrum. Methods, in press. 5 EURORAD Charge Loss Detector, User Manual, Strasbourg, 1992. 6 G. Ottaviani, C. Canali, C. Jakobini, A. Alberigi Quaranta and K. Zarfio, J. Appl. Phys., 44 (1973) 360. 7 D. Vartsky and E Siffert, Nucl. Instrum. Methods, A263 (1988) 457.
Materials &'ience and Engineering, B16( 1993': 296-3(} 1
Compensation of trapping losses in CdTe detectors M. Richter, P. Siffert and M. Hage-Ali Centre de Recherches Nucleaires (IN2P3)--Laboratoire PtOt~E ~(~)~'Rdu CNRS No. 292), BP 20, F-6 7037Strasbourg Cedex (France)
Abstract Energy resolution and photopeak efficiency of planar CdTe ttlt~lL~tf ~di~iiion spectrometers are degraded by charge trapping effects in the bulk of the detector. Chari~ 1o~ ~ g ~ t f i o n methods result in an enhancement of energy resolution and photopeak efficiency, but these t e c h n l q ~ O[b~tate only with certain detectors. In this article we present data from dual-parameter gamma-ray sp~trotll~l'y ~ad time-of-flight experiments to characterize these devices. A computer model of the charge collection inside the detector will be discussed.
1. Introduction Cadmium telluride (CdTe) is a material of interest as a highly sensitive, room temperature-ope~tin8 gamma-ray spectrometer. Modem detectors offer good stability and energy resolution. The best energy resolution up to now of about 0.5% at 662 keV has been achieved by using a slightly cooled detector with a p-i-n structure [1]. However, owing to the small electron and hole mobilities in the p-type material generally used, the sensitive region of these detectors is only 0.1-0.3 mm thick. Thus, detection efficiency is rather limited. In CdTe detectors having a metal-semiconductormetal (m-s-m) structure the depletion layer can be quite thick (about 1-2 mm). Therefore these devices are much more sensitive; however, the energy resolution and photopeak efficiency of such a thick planar CdTe detector are degraded owing to poor hole transport properties. Consequently, the field of application is still limited. Different approaches to detector geometry and pulse processing techniques have been tested to overcome these shortcomings [2, 3]. However, mostly they did not result in much better resolution or they caused severe problems with detector stability and efficiency loss. Charge loss correction methods are the most promising [4]. They are based on the assumption that poor energy resolution is mainly related to trapped holes, while the electrons are collected almost without any losses. Because of the much higher mobility of the electrons, the overall charge collection time is determined by the collection time of the holes. The relation between the energy loss fraction and the charge collection time has been measured experimentally and based 0921-5107/93/$6.00
on these data we could establish a correction function. This results in a tremendous improvement in energy resolution and photopeak efficiency. However, this correction method still demands devices made from nlat~rials with sufficiently high hole mobility. In this lyaper, we present some recent results performed some of these "good" detectors.
2. Dual-parameter spectrometry The goal of the experiment was to investigate the variation of the spectrum shape as a function of the charge collection time. Using the Charge Loss Correcter of the firm EURORAD [5], which provides for an optional second output of the risetime information in coincidence with the pulse height at the energy output, we measured dual-parameter spectra of different radiation sources with gamma-ray energies from 60 keV (241Am) up to 662 keV (137Cs). The spectra show clearly that the initial result can be regarded as a summation of subspectra with shifted photopeaks. The subspectrum near the shortest risetimes offers the best energy resolution and peak-toCompton ratio (Fig. 1). This matches the experience gained with resolution enhancement using risetime selection systems [3, 4]. Spectra measured with longer risetimes have worse resolution and spectrum shape. Unfortunately, this limits the performance of charge loss correction methods and demands a pulse preselection to suppress pulses with collection times that are too long. The application determines a compromise between efficiency and energy resolution [5]. The photopeak intensity of these subspectra decreases nearly exponentially with increasing charge © 1993 - Elsevier Sequoia. All rights reserved
M. Richter et al,
/
Compensating trapping losses in CdTe detectors
137-Cs spectra measured with different nseame windows
2~s
297
122keV m,
./k.__ ./k__
A
,t0oos 56
100
150
20o
25O
30O
35O
400
450
500
ehaaae.l number
Fig. 1. This dual parameter spectrum of a ~37Cssource demonstrates that the untreated energy spectrum measured with a CdTe detector can be regarded as a superposition of shifted subspectra resulting in the low energy tailing of the photopeaks. Each subspectrum is generated in a different layer of the detector.
Fig. 3. Dual parameter spectrum of a 57C0 source. Compared with the corresponding ~37Csspectrum of Fig. 2, the intensity of the photopeak decays faster. The constant of this exponential function corresponds well with the absorption coefficient.
662kcV
"-'t)O.7
Fig. 2. Dual parameter spectrum of a 137Cssource. The intensity of the 662 keV photopeak decays following the absorption
Fig. 4. Dual parameter spectrum of a 137Cs source. This point of view shows clearly the linearity between photopeak shift and charge collection time.
curve.
collection time (Figs. 2 and 3). The constant of this exponential function is approximately equal to the absorption coefficient of CdTe for this energy. The error can be explained by the influence of the inhomogenous electrical field inside the detector (see below). This indicates that the phonon energy is absorbed at one point. The relative charge loss depends only on the depth of the carrier generation and not on its initial number. T h e low energy tail of the photopeaks appears as a superposition of shifted subspectra with decaying intensity. As already mentioned formerly, the photopeak shift, i.e. the relative charge loss, is linearly proportional to the risetime a n d d o e s not depend on radiation energy (Figs. 4 and 5). Of course the question of why it is linear still remains.
3. Current pulse measurements To get some more information about the shape of the electrical field inside the detector we must follow the path of the carders from the point of generation to the contacts. One way to do this is to measure the current pulse. The current is proportional to the number of carriers and their speed. The speed is the product of mobility and electrical field. This means that for a constant number and mobility of carriers the current pulse I(t) gives directly the function E(t). If we arrange a way for the charge to be transported through the whole detector by exclusively one carrier type, then the current pulse I(t) is proportional to E(x). We can fulfil these conditions if we irradiate the negative-biased surface of a detector with alpha-parti-
298
,~t. Richter et aim
/' ('ornpensating trapping losses in ('dTe detectors 0.04
$5 - 2A Vdet = 125V
~ 0.03
o.o2 0.01
~
0 -0.01
0
1
2
4
6
7
8
9
i
i
!
time [s]
008
oo.o W 0.04
~_00021 ; 0
Fig. 5. Dual parameter spectrum of a 57Co source. It is shown that the linear peak shift does not depend on gamma-ray energy.
cles or soft X-rays. The charge will be transported by electrons to the positive contact. For a sufficiently high bias voltage the carrier transit time is small in comparison with its lifetime. Thus the shape of the electron current pulse is mainly influenced by the shape of the electrical field. In our experiments we used 2 mm thick CdTe detectors with platinum contacts. The bias voltage varied from 100 V to 300 V. The electron lifetime was measured to be at least 1 Its. A fast current-sensitive preamplifier in a closed loop configuration has been used for the measurements. A high open loop gain ensures short risetimes and accuracy. The results were rather unusual (Fig. 6). The electrical field has its maximum near the negative contact of the detector and decays more or less exponentially in the direction of the positive side. This is completely contradictory to former investigations of detector polarization [6, 7]. We repeated these experiments with many "good" detectors, that is, with devices which work well with the E U R O R A D Charge Loss Correctot. The results were always similar. Further, we observed also the hole current pulses (Fig. 7). Although the collection time of the generated charge is much longer, the current decays only slightly. For higher detector bias voltages the hole current is rising with time. Thus, the higher speed of the holes near the negative contact can obviously compensate for the number of carriers lost by trapping. This also means that the speed of the holes in all layers of the detector is still proportional to the electrical field. Another unexpected observation was the ratio of the currents of electrons to that of holes. A voltage pulse at the output of a commonly used charge-sensitive preamplifier represents the integral over the detector current pulse. If we compare the slopes of the fast and slow fractions of such a pulse we get a ratio of about 6
...................
10 x l 0 "7
t
i ................ i ................ i ................ i ............... ! ............... ; ............... i ................ i ..............
i;i!i
i
,
2
4
5 time [s]
6
7
8
9
10 x l 0 "7
Fig. 6. Current response from alpha-particle irradiation of the negative detector contact. The electron current pulse decays much faster as we would expect from the carrier lifetime. Even for a shorter collection time (see lower curve) the pulse shape does not change substantially. This phenomenon can be explained by a non-homogenous electrical field inside the detector.
2 xl0"~
i
i
-1
,
,
.............. i .............. ~..........
0
1
2
,
SP-2A V dct = 125V
i ......
'
3
4
............... i ................ i ................ ~,...............
6
7
8
9
t [us]
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z
,
.............. ~ ............... i ........
. ~
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.
.......~................i................i...............+...............~...............i..............
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-1 0
1
2
3
4
5 t [us]
6
7
8
9
10 x l 0 "6
Fig. 7. Hole current pulse after charge generation at the positive detector contact. Although the holes move much slower than the electrons we do not observe a current decay. The electrical field obviously accelerates the holes in the direction of the negative
contact and compensates in such a way for the number of cartiers lost by trapping. This does not mean that the hole collection efficiency becomes better, as it depends only on the final collection time, but it proves that the electrical field increases against the negative contact.
to 12. For the penetrating 662 keV radiation of a ~37Cs source we got similar results using the current amplifier (Fig. 8). In experiments with alpha particles we measured an electron current 50 times higher than that of holes. This indicates the existence of a dead layer near the positive contact. Thus, only a small fraction of the
M. Richter et al. SS-2A Vdet
>
/
Compensating trapping losses in CdTe detectors xl05
= 125V
1
I'
i
'
i
i
5
un=1100 up--80 d=£1.19 xo=0 k=5 h--0.002
111 I \ I \ 12 t ~
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3 Eo=t50OV/cm
I
3 re(t)
U
i
i
i
4
6
i
8
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time I u']
Fig. 8. The detector was irradiated with a ~37Cs source. The current pulse demonstrates the ratio of electron and hole current at a point in the middle of the detector.
generated carriers reaches the internal collection field and the hole current is much smaller. T h e main result of the current measurements was the discovery of the fast polarization of the used detectors. T h e electrical field has its maximum at the negative contact and is decaying exponentially. This results in faster hole collection and in some unusual current pulse shapes.
4. Modelling As a result of these calculations we expected a better understanding of the influence of the different detector parameters on the charge collection efficiency. T h e basis of our detector model comes from the observation of the current pulses. By varying the model carrier properties, such as mobility and lifetime, and also the field distribution, we fitted the calculated curves to the actual measured pulses. T h e final model matches well our experiences of real detectors, in which we have: Electrons: Un = 1 100 cm 2 V- 1 s- 1 _- constant rn = 1 ~S Holes:
up0 = 80 cm 2 V - 1 s- 1 up(x) = f ( E ) = up0 + h * E ( x ) r p - - 1 ~s
Field:
E = E 0 * exp( - k* x)
Detector:
thickness d = 1.9 m m negative contact: x = 0
With constant hole mobility and a realistic lifetime it was not possible to reconstruct the observed pulse shapes. Oltaviani et al. [6] found a relation between the electrical field and the hole mobility (Poole-Frenkel
0I
0
1
2
3 C011eCtlOtl lime {s]
4
5 x l 0 "7
Fig. 9. Electron current pulses in(t) of the model detector calculated for different values of the electrical field at the negative contact. These correspond to detector voltages of 100 V, 200 V and 300 V, for i = 1, 2 and 3 respectively. The resulting curve is the superposition of trapping loss and the decay of carrier speed. effect). In the case of a high electrical field inside a biased detector this relation can be linearized. To display the current pulse we have to calculate the speed and n u m b e r of carriers in the time period tcon between the generation of charge at the point x 0 and its recombination at the contacts. T h e fraction of the carriers reaching the contacts is determined only by the collection time. n = n0* exp( - tcon/r)
(1)
Assuming the proportionality of speed and electrical field we can write for the electrons: v(t, x0)=
1 t*k + 1/V(Xo)
(2)
For the holes the integrals are more complicated owing to the non-constant mobility. We solved the equations numerically. Figures 9 - 1 1 present current pulses for different values of the electrical field generated at different positions inside the detector. T h e current pulses for x = 0 and x = d corresponds to the experiments with alpha particles. T h e electron current is a good match to the real data. T h e main difference is the presence of noise and the limited bandwidth of the current amplifier used for the measurements. T h e important discrepancy for the holes can be explained by the existence of a thin dead layer under the positive contact which has been neglected in the calculation. We were more interested in the principal pulse shape. For charge generation in the middle of the detector (Figs. 8 and 11) the model is in agreement with the experimental data.
300
:14. Richter et al. xl05
/
('ompensating trapping losses in CdTe detectors
un=ll00up=80 d---O.19 xo=O.19 k=5 h=0.002
1.8
0.9
;I
1.6 1.4
/'
/; /"
1.2
3 ip(t)
J
1
un= 1100 up=80 d=0.19 k=5 h---0.002
II
1 1 E'b=500V/cm
0.8
2 Eo=1000V/cm
0.7
3 Eo= I500V/cm
0.6
,
i
3
i
0.5 0.8
0.4-
0.6
............ !..............
0"4 Il i L.
: 2ip(t)
---
0
2
3
3 Eo=1500V/crn
0I
0
4
collectiontame [s]
xlO "6
Fig. 10. Calculated hole current pulses/p(t). Near the negative contact the holes are moving faster.The number of carriers lost by trapping can be compensated. For higher electricalfields this effectis more impressivc.
xl05
un=ll00 up=80 d=0.19 xo~0.1 k=5 h~0.002
10
8 \
1 Ec~500V/cm 3 in(t)
2 Ec~ 1000V/cm
6 \\
3 Eo=1500V/cm
\l 4 ~m(t) ~ .
,,i 3 ip(t)
[l'~m
......
.....
........
0 .... l--k ..... !b-, .........
0
0.2
i
0.1
lip(t) 1
....
2 Eo=1000V/cm i
0"2 / .....
2
0.3
0.2
0.4
1 "°(" ,4 ......
0.6
i tp(t) ........
0.8
........
i
coll~laon time [s]
-, . . . . . . . . .
1.2
,. . . . . . .
1.4
:-r ........
1.6
,
1.8 xlO ~
Fig. 11. For this calculation a charge generation in the middle of the detector has been assumed. Both carder types take part in the charge collection (electron current: solid line; hole current: dashed line).
The resulting curves of collected charge vs. collection time of the adapted detector model are presented in Fig. 12. They tend to be linear. The value of the applied electrical field changes only the gradients of the curves, but not their fundamental shape.
5. Discussion
The investigated detectors have followed the evolution of technology since 1983. They are made from highly resistive material which has been grown in a
015
i
~;
i
2;
3
charge coll~tion tame Is]
3;
i
;.5 xl0 "6
Fig. 12. The function of the collected charge vs. collection time of the modelled detector tends to be linear.
travelling heater method (THM) process under Te pressure. As contact material platinum or gold is used. The sensitive surface area is between 25 mm and 56 mm 2. The devices are mostly 2 mm thick. The best energy resolution can be achieved if the negative side of the detectors is irradiated. With current pulse measurements it was found that the electrical field inside the detectors has its maximum at the negative contact. Because we still obtained a signal from alpha-particle irradiation of the positive side we think that the "dead layer" there is very thin. This is totally contradictory to former investigations [7]. Only for an old detector made from n-type material with Al contacts did we observe the same direction of polarization. The T H M material is normally suspected to be p-type but experimental confirmation is rather difficult owing to its high resistivity. The influence of contact material is not so clear yet. For detectors from one CdTe ingot the orientation of polarization changes if we contact them with gold instead of platinum; for another ingot the detectors polarize independently of the contact material in the "wrong" direction. Analysis methods such as thermal scanning calorimetry or secondary ion mass spectrometry did not offer suspicious differences. Furthermore, we could not measure a change in the detection efficiency vs. time. So we assume that the polarization is a very fast process. Up to now we are unable t o explain these phenomena. Although nearly all newer detectors show this inverted polarization, only a small number of them provide good results with the linear charge loss correction method. As also proved by the model, only detectors with a sufficiently high mobility-lifetime product for holes work well.
M. Richter et al.
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Compensating trapping losses in CdTe detectors
301
To select detectors for the correction, we irradiated them with the deeply penetrating 662 keV gamma rays of a 137Cs source. We observed the output pulses of a normal charge-sensitive preamplifier. If they are composed of slow and fast rising fractions it is probable that this detector works well with our charge loss correction circuit.
on the charge collection efficiency has been investigated. The function of relative charge loss vs. charge collection time of this model detector is nearly linear and correlates well with experimental data. The observation of fast polarization in CdTe detectors made from highly resistive p-type material is still incomprehensible.
6. Conclusion
References
By means of dual-parameter spectroscopy the function of relative charge loss vs. collection time was measured. The experiments demonstrated once more the linearity, and independence of photon energy, of relative charge loss. With time-of-flight measurements it has been discovered that the electrical field inside some "good" detectors is exponentially shaped. By means of a computer model the influence of this field distribution
1 A. Kh. Khusainov, Nucl. Instrum. Methods, in press. 2 K. Zanio, Rev. Phys. Appl., 12(1977) 343. 3 U. Hagemann, R. Berndt and R. Arlt, Kernenergie, 31 (1988) 54. 4 M. Richter and P. Siffert, Nucl. Instrum. Methods, in press. 5 EURORAD Charge Loss Detector, User Manual, Strasbourg, 1992. 6 G. Ottaviani, C. Canali, C. Jakobini, A. Alberigi Quaranta and K. Zarfio, J. Appl. Phys., 44 (1973) 360. 7 D. Vartsky and E Siffert, Nucl. Instrum. Methods, A263 (1988) 457.