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Charge collection efficiency in mercuric iodide nuclear detectors
NLCLEAR
INSTRUMENTS
AND
METHODS
167 ( 1 9 7 9 )
423-426;
(~) N O R T H - H O L L A N D
PUBLISHING
CO.
CHARGE COLLECTION EFFICIENCY IN MERCURIC IODIDE NUCLEAR DETECTORS I. BEINGLASS ~ and M. SCHIEBER Hebrew University o f Jerusalem, School o f Applied Science and Technology, Israel Received 9 April 1979 and in revised form 13 August 1979 The contribution of incomplete charge collection ( 1 - q)) to the line broadening AEco I of HgI2 nuclear detectors has been analysed after subtracting the contribution of the electronic and statistical fluctuation. The measurement of AEco I versus 1 - r / for a given gamma radiation energy corresponds to 3Eco 1 = a ( l - r / ) for Ey ranging from 59.6 up to 662 keV where a is a calculated parameter.
1. Introduction The influence of carrier collection efficiency r/on the energy resolution, ZlEcol, and photopeak line shape of gamma nuclear radiation detectors has been studied thoroughly in germanium, (Ge) detectors 1-5). ...... It has been found that in Ge detectors the contribution of AEcol on the measured full width at half maximum, f w h m , was minimal due to the perfection of the detector crystals. Thus in Ge the statistical fluctuation of electron and hole creation AEv is the main contribution to AE. In mercuric iodide (HgI2) detectors similar studies were made by Slapa et al.6), but only for the 5.9 keV X-ray energy radiation of 55Fe.These studies have shown that the main contribution to AE is the incomplete charge collection, 1 - r/. However, irradiation with low energy X-rays only represents the photoelectric interaction which occurs on the surface of HgI2 detectors and almost electron trapping alone is involved. Therefore, it was considered important to study the influence of ;7 on zlE for higher gamma ray energies, so that we could also observe the photoelectric interaction in the bulk of HgI2 and other trapping effects. The present paper describes the behaviour of 3E~o~ at gamma ray energies ranging between 59.6-662 keV. 2. Theoretical consideration A large amount of work on trapping and the charge collection effect has been done on Ge detectors. Day et al. 1) have analysed the effect of traps on the detector performance. In their analysis, they made the following assumptions: * Present address: Intel Corporation, 3065 Bowers Ave., Santa Clara, CA 95051, U.S.A.
(1) the electric field in the detector is uniform. (2) the traps are uniformly distributed in the detector. (3) The radiation is uniformly excited in the detector. The analysis of trapping in the detector involves the parameters 2n and 2p (the mean free path of electron and hole before trapping) where 2 = tzrE, is the mobility, r is the mean free time and E is the electric field on the detector. The resulting expressions for general trapping effects are rather complicated. Armantrout 5) and Makovski 7) suggested some amount of simplification based on the following assumptions : (1) 2n and 2p > crystal thickness. (2) Trapping of one type of carrier is predominant. After some calculation one can find from Armantrout's work that 4'5)
AEco, = a ( 1 - q ) E .
(1)
Henck et al. 6) applied this formula by using results obtained with the 122 keV line of 57Co radioactive source and the 662 keV line of 137CS. However their results show a different behaviour for AEco~: AEco 1 =
a (1 - - q ) E
1/2 .
(2)
The total energy resolution can be expressed by the well known relation: ( A E ) 2 = ( A e e l ) 2 + ( A E F ) 2 ,--1-(Aecol) 2 ,
(3)
where AEe~ is the .contribution due to the electronic noise in the detector amplifier system and AE~o~ and AEv where defined in the introduction. The present results however, do show that AEcot used for HgI2 detectors is more complex than for Ge detectors as will be shown later in the paper.
424
1. BEINGLASS AND M. SCHIEBER
3. Experimental Mercuric iodide crystals were grown from repeated sublimation purified and iodine 8) treated raw material in a horizontal 9) furnace using the vapour phase temperature oscillation method~°). The crystals were made into a detector either by sawing or cleaving into plates, etching in a KI water solution contacting with aquadag, and encapsulating in Humiseal. The detectors were connected to a Seforad Type 105 preamplifier and to a Tennelec Type 205 main amplifier. They were biased up to 2000 V from an Elscint H V - N - 1 A power supply. For this experiment 6 detectors were used having a thickness of about 0.5 m m and an area of 2 0 - 4 0 m m 2.
i.o-
o.9o,de>o o4 08-
/
/ ~ 0.3 0'2'
0.1
'~ 4
~ ~ ,5 ,~ ,~, ~ ,~, ~o ;.2 ',,,o-' '
[Vott-'J
Fig. 1. Energy resolution of the detector, dEo, expressed as full width at half maximum, fwhm, in (keV) as a function of the inverse bias voltage [1/V(V-1)].
4. The Fano factor In order to get the Fano factor, F, relation (3) can be written as: (AEd) 2 = (AE) 2 - ( A E e l ) 2 = (AEF) 2 4- ( A E c o , ) 2 , (4)
In order to find AEF, AEcot must be negligible. This can be done by extrapolating to infinite field, under the assumption that AEco~becomes zero at an infinite field11). Fig. 1 shows AE, as a function of 1/V. The bias voltage independent part of AEd is then determined by the extrapolated intercept of the AEd versus 1/V curve on the AE~ axis. Using relation (5) one can get the value of 0.45. This
where AEd is the energy resolution of the detector only. AEF is defined as:
AEF = 2.355 (wE~F)'/2 ,
55Ee 5.9KEY line CD-22
(5)
where w is the energy per creation pair of an elect r o n - h o l e and F is the Fano factor. IO'O 8"0 60
"1-
0.'2'
0,11
2
3
4
5
6
8
I0
2
3
4
5
6
e
Energy (KeV) Fig. 2. Energy resolution due to statistical fluctuations in pair formations, ray energy, Ey (keV) for different values of the Fano factor F.
i0
2
AEF, expressed as
3
4
5
6
8
i0 3
fwhm in keV as a function of gamma
425
CHARGE COLLECTION EFFICIENCY TABLE 1
TABLE 2
Source E(keV) AEF(keV)
55Fe
241 Am
57Co
137Cs
5.9 0.249
59.6 0.79
122 1.131
662 2.635
Ge a(keV) zlEres (keV)
value is in agreement with the value of 0.51 determined by Slapa et al. 6) and F = 0.47 determined by Dabrowski et a1.12). Figure 2 plots AEv as a function of E~, the photon energy, for different values of F as a paramete.r. Using the data of fig. 2 with F = 0.45 one can calculate the contribution to the line broadening caused by the statistical fluctuation in creation of hole-electron pairs, for different photon energies as summarized in table 1. One can see that AEv represents about 50% of the total fwhm for low energies13),whereas at 662 keV where the average fwhm is about 15 keV AEv is only about 17%.
5. Incomplete charge collection Rewriting relation 3) in the form of
AE,o ' = (AE z_AEel_2 AE~)I/z
(6)
and subtracting the electronic noise zlEe~ and the statistical fluctuation broadening AEv from the total fwhm of the detected LIE one could measure AEco,,
60 keV 1.2× 102 0
122 keV 3×102 0
662 keV 6.6× 102 0
i.e., the contribution of the line broadening caused by incomplete charge collection ( 1 - r/). Figure 3 shows a linear plot of AEco~ as a function o f 1 - / 7 for various energies of gamma rays o f e.g., 59.6, 122 and 662 keV. Slapa et al., 6) did perform similar experiments but only at a lower energy of 5.9 keV and measured a similar linear relation between AEco~ and 1 - / 7 . For the lower energies of 241Am and 57Co the plot intercepts at the value zlEco, = 0 when 1 - / 7 = 0 but for the higher energies of the 137Cs source it does not intercept at the origin. Two problems can be seen from these results: (1) " a " is not the same for all energies - see table 2. (2) The occurrence of a residual resolution AE .... which for 662 keV transforms AE~o] to a changed AEco~ given as:
AE'¢ol = AEcol+ AE ....
(7)
where AlEres = 5 keV and which may be concerned with the departure from the symmetry of the gaussian shape of the 662 keV photopeak as can be seen in fig. 5.
~D
5¥o 2 41A /
24
24 e
2.0 1.8 16
>~
> 12 l..a
UA 08
/
r37cs
0.6 0.4
0
--
I
I0
20 x I0-3
0
20 x 10-3
I-r[ Fig. 3. Energy resolution AEco I (keV) due to incomplete charge collection ( 1 - r/) as a function of 1 - r / for various energies measured with detector HR-III-31 #10.
426
I. BEINGLASS AND M. S C H I E B E R
~'
I-~.-" 5 X I0 " 3
I0,
;~
~
662 keV '~92 keV
c
~ 2,(~ k e V - -
m Ua
FtlERGY Fig. 5, Spectrum of 137Cs detected with the HgI 2 crystal.
,;o'
,loz
t/o~
'
E (K6V)
Fig. 4. Energy resolution AEco1 (in keV) as a function of radiation energy, Ey (keV) as a function of radiation energy, Ey (keV) for a constant value of (1 - r / ) 5 × 10-3 for detector HR-III-31 #10.
One can further look into AEcot and try to see how it behaves as a function of energy. Fig. 4 is a plot of AEco~ as a function of E for a constant value of l - r / on a l o g - l o g scale. The line follows the equation : AEco ~ = BE",
(8)
where n < 1. For Ge detectors the value of n is 0.5, but for HgI2 one gets 1 > n > 0 . 5 , which is caused by the parameter AEre s and by changes of the " a " factor which varies from energy to energy due to changes in the ( 1 - r / e ) / ( 1 - r / n ) ratio. Nevertheless it is worthwhile to mention that in the better HgI2 detectors n < 1 and one can speculate that further improvements should bring down the value of n closer to 0.5. 6. Conclusions By writing the square energy resolution as a sum of the square parts of the electronic noise, the fluctuation in the pair formation of holes-electrons, and the incomplete charge collection one can find
the values for the Fano factor. The present calculated Fano factor agrees with the data published by Slapa et al.,6). The incomplete charge collection according to Armantrout 5) and Henck 4 et al., shows an expected difference between the nuclear performance of HgI2 and Ge detectors which stems from the difference in the crystal quality and homogeneity of the two detectors. References 1) R. B. Day, G. Dearnaly and J. M. Palms, IEEE Trans. Nucl. Sci. NS-14 (1967) 487. 2) G.A. Armantrout and H.W. Thompson Jr., IEEE Tran. Nucl. Sci. NS-|7 (1970) 165. 3) R. Tramell and F. J. Walter, Nucl. Instr. and Meth. 76 (1969) 317. 4) R. Henck, D. Gutknecht, P. S. Siffert, L. DeLaet and W. Schoenmackers, IEEE Trans Nucl. Sci. NS-17 (1970). 5) G. A. Armantrout, UCRL-71508 (1969). 6) M. Slapa, G.C. Huth, W. Seibt, M. Schieber and P.J. Randtke, IEEE Trans. Nucl. Sci. NS-23 (1976) 102. 7) L. L. Makovski, N. B. Strokam and N. I. Tisnek, Sov. Phys Semicond. 3 (1970) 928. 8) I. Beinglass, G. Dishon, A. Holzer and M. Schieber, J. Cryst. Growth 42 (1977) 166. 9) M. Schieber, 1. Beinglass, G. Dishon and A. Holzer, in Crystal Growth and Mat. Proc. First European Conf. on Crystal growth, eds., S.E. Kaldis and H.J. Scheel (North-Holland, Amsterdam, 1977)p. 279. L0) M. Schieber, W. F. Schnepple and L. Van Den Berg, J. Cryst. Growth 33 (1976) 145. II) H.R. Zulliger and D.W. Aitken, IEEE Trans. Nucl. Sci. NS-17 (1970). 12) A.J. Dabrowski and G.C. Huth, IEEE Trans. Nucl. Sci. NS-25 (1978) 205. 13) 1. Beinglass, G. Dishon, A. Holzer, S. Ofer and M. Schieber, Appl. Phys. Lett. 30 (1977) 611.
INSTRUMENTS
AND
METHODS
167 ( 1 9 7 9 )
423-426;
(~) N O R T H - H O L L A N D
PUBLISHING
CO.
CHARGE COLLECTION EFFICIENCY IN MERCURIC IODIDE NUCLEAR DETECTORS I. BEINGLASS ~ and M. SCHIEBER Hebrew University o f Jerusalem, School o f Applied Science and Technology, Israel Received 9 April 1979 and in revised form 13 August 1979 The contribution of incomplete charge collection ( 1 - q)) to the line broadening AEco I of HgI2 nuclear detectors has been analysed after subtracting the contribution of the electronic and statistical fluctuation. The measurement of AEco I versus 1 - r / for a given gamma radiation energy corresponds to 3Eco 1 = a ( l - r / ) for Ey ranging from 59.6 up to 662 keV where a is a calculated parameter.
1. Introduction The influence of carrier collection efficiency r/on the energy resolution, ZlEcol, and photopeak line shape of gamma nuclear radiation detectors has been studied thoroughly in germanium, (Ge) detectors 1-5). ...... It has been found that in Ge detectors the contribution of AEcol on the measured full width at half maximum, f w h m , was minimal due to the perfection of the detector crystals. Thus in Ge the statistical fluctuation of electron and hole creation AEv is the main contribution to AE. In mercuric iodide (HgI2) detectors similar studies were made by Slapa et al.6), but only for the 5.9 keV X-ray energy radiation of 55Fe.These studies have shown that the main contribution to AE is the incomplete charge collection, 1 - r/. However, irradiation with low energy X-rays only represents the photoelectric interaction which occurs on the surface of HgI2 detectors and almost electron trapping alone is involved. Therefore, it was considered important to study the influence of ;7 on zlE for higher gamma ray energies, so that we could also observe the photoelectric interaction in the bulk of HgI2 and other trapping effects. The present paper describes the behaviour of 3E~o~ at gamma ray energies ranging between 59.6-662 keV. 2. Theoretical consideration A large amount of work on trapping and the charge collection effect has been done on Ge detectors. Day et al. 1) have analysed the effect of traps on the detector performance. In their analysis, they made the following assumptions: * Present address: Intel Corporation, 3065 Bowers Ave., Santa Clara, CA 95051, U.S.A.
(1) the electric field in the detector is uniform. (2) the traps are uniformly distributed in the detector. (3) The radiation is uniformly excited in the detector. The analysis of trapping in the detector involves the parameters 2n and 2p (the mean free path of electron and hole before trapping) where 2 = tzrE, is the mobility, r is the mean free time and E is the electric field on the detector. The resulting expressions for general trapping effects are rather complicated. Armantrout 5) and Makovski 7) suggested some amount of simplification based on the following assumptions : (1) 2n and 2p > crystal thickness. (2) Trapping of one type of carrier is predominant. After some calculation one can find from Armantrout's work that 4'5)
AEco, = a ( 1 - q ) E .
(1)
Henck et al. 6) applied this formula by using results obtained with the 122 keV line of 57Co radioactive source and the 662 keV line of 137CS. However their results show a different behaviour for AEco~: AEco 1 =
a (1 - - q ) E
1/2 .
(2)
The total energy resolution can be expressed by the well known relation: ( A E ) 2 = ( A e e l ) 2 + ( A E F ) 2 ,--1-(Aecol) 2 ,
(3)
where AEe~ is the .contribution due to the electronic noise in the detector amplifier system and AE~o~ and AEv where defined in the introduction. The present results however, do show that AEcot used for HgI2 detectors is more complex than for Ge detectors as will be shown later in the paper.
424
1. BEINGLASS AND M. SCHIEBER
3. Experimental Mercuric iodide crystals were grown from repeated sublimation purified and iodine 8) treated raw material in a horizontal 9) furnace using the vapour phase temperature oscillation method~°). The crystals were made into a detector either by sawing or cleaving into plates, etching in a KI water solution contacting with aquadag, and encapsulating in Humiseal. The detectors were connected to a Seforad Type 105 preamplifier and to a Tennelec Type 205 main amplifier. They were biased up to 2000 V from an Elscint H V - N - 1 A power supply. For this experiment 6 detectors were used having a thickness of about 0.5 m m and an area of 2 0 - 4 0 m m 2.
i.o-
o.9o,de>o o4 08-
/
/ ~ 0.3 0'2'
0.1
'~ 4
~ ~ ,5 ,~ ,~, ~ ,~, ~o ;.2 ',,,o-' '
[Vott-'J
Fig. 1. Energy resolution of the detector, dEo, expressed as full width at half maximum, fwhm, in (keV) as a function of the inverse bias voltage [1/V(V-1)].
4. The Fano factor In order to get the Fano factor, F, relation (3) can be written as: (AEd) 2 = (AE) 2 - ( A E e l ) 2 = (AEF) 2 4- ( A E c o , ) 2 , (4)
In order to find AEF, AEcot must be negligible. This can be done by extrapolating to infinite field, under the assumption that AEco~becomes zero at an infinite field11). Fig. 1 shows AE, as a function of 1/V. The bias voltage independent part of AEd is then determined by the extrapolated intercept of the AEd versus 1/V curve on the AE~ axis. Using relation (5) one can get the value of 0.45. This
where AEd is the energy resolution of the detector only. AEF is defined as:
AEF = 2.355 (wE~F)'/2 ,
55Ee 5.9KEY line CD-22
(5)
where w is the energy per creation pair of an elect r o n - h o l e and F is the Fano factor. IO'O 8"0 60
"1-
0.'2'
0,11
2
3
4
5
6
8
I0
2
3
4
5
6
e
Energy (KeV) Fig. 2. Energy resolution due to statistical fluctuations in pair formations, ray energy, Ey (keV) for different values of the Fano factor F.
i0
2
AEF, expressed as
3
4
5
6
8
i0 3
fwhm in keV as a function of gamma
425
CHARGE COLLECTION EFFICIENCY TABLE 1
TABLE 2
Source E(keV) AEF(keV)
55Fe
241 Am
57Co
137Cs
5.9 0.249
59.6 0.79
122 1.131
662 2.635
Ge a(keV) zlEres (keV)
value is in agreement with the value of 0.51 determined by Slapa et al. 6) and F = 0.47 determined by Dabrowski et a1.12). Figure 2 plots AEv as a function of E~, the photon energy, for different values of F as a paramete.r. Using the data of fig. 2 with F = 0.45 one can calculate the contribution to the line broadening caused by the statistical fluctuation in creation of hole-electron pairs, for different photon energies as summarized in table 1. One can see that AEv represents about 50% of the total fwhm for low energies13),whereas at 662 keV where the average fwhm is about 15 keV AEv is only about 17%.
5. Incomplete charge collection Rewriting relation 3) in the form of
AE,o ' = (AE z_AEel_2 AE~)I/z
(6)
and subtracting the electronic noise zlEe~ and the statistical fluctuation broadening AEv from the total fwhm of the detected LIE one could measure AEco,,
60 keV 1.2× 102 0
122 keV 3×102 0
662 keV 6.6× 102 0
i.e., the contribution of the line broadening caused by incomplete charge collection ( 1 - r/). Figure 3 shows a linear plot of AEco~ as a function o f 1 - / 7 for various energies of gamma rays o f e.g., 59.6, 122 and 662 keV. Slapa et al., 6) did perform similar experiments but only at a lower energy of 5.9 keV and measured a similar linear relation between AEco~ and 1 - / 7 . For the lower energies of 241Am and 57Co the plot intercepts at the value zlEco, = 0 when 1 - / 7 = 0 but for the higher energies of the 137Cs source it does not intercept at the origin. Two problems can be seen from these results: (1) " a " is not the same for all energies - see table 2. (2) The occurrence of a residual resolution AE .... which for 662 keV transforms AE~o] to a changed AEco~ given as:
AE'¢ol = AEcol+ AE ....
(7)
where AlEres = 5 keV and which may be concerned with the departure from the symmetry of the gaussian shape of the 662 keV photopeak as can be seen in fig. 5.
~D
5¥o 2 41A /
24
24 e
2.0 1.8 16
>~
> 12 l..a
UA 08
/
r37cs
0.6 0.4
0
--
I
I0
20 x I0-3
0
20 x 10-3
I-r[ Fig. 3. Energy resolution AEco I (keV) due to incomplete charge collection ( 1 - r/) as a function of 1 - r / for various energies measured with detector HR-III-31 #10.
426
I. BEINGLASS AND M. S C H I E B E R
~'
I-~.-" 5 X I0 " 3
I0,
;~
~
662 keV '~92 keV
c
~ 2,(~ k e V - -
m Ua
FtlERGY Fig. 5, Spectrum of 137Cs detected with the HgI 2 crystal.
,;o'
,loz
t/o~
'
E (K6V)
Fig. 4. Energy resolution AEco1 (in keV) as a function of radiation energy, Ey (keV) as a function of radiation energy, Ey (keV) for a constant value of (1 - r / ) 5 × 10-3 for detector HR-III-31 #10.
One can further look into AEcot and try to see how it behaves as a function of energy. Fig. 4 is a plot of AEco~ as a function of E for a constant value of l - r / on a l o g - l o g scale. The line follows the equation : AEco ~ = BE",
(8)
where n < 1. For Ge detectors the value of n is 0.5, but for HgI2 one gets 1 > n > 0 . 5 , which is caused by the parameter AEre s and by changes of the " a " factor which varies from energy to energy due to changes in the ( 1 - r / e ) / ( 1 - r / n ) ratio. Nevertheless it is worthwhile to mention that in the better HgI2 detectors n < 1 and one can speculate that further improvements should bring down the value of n closer to 0.5. 6. Conclusions By writing the square energy resolution as a sum of the square parts of the electronic noise, the fluctuation in the pair formation of holes-electrons, and the incomplete charge collection one can find
the values for the Fano factor. The present calculated Fano factor agrees with the data published by Slapa et al.,6). The incomplete charge collection according to Armantrout 5) and Henck 4 et al., shows an expected difference between the nuclear performance of HgI2 and Ge detectors which stems from the difference in the crystal quality and homogeneity of the two detectors. References 1) R. B. Day, G. Dearnaly and J. M. Palms, IEEE Trans. Nucl. Sci. NS-14 (1967) 487. 2) G.A. Armantrout and H.W. Thompson Jr., IEEE Tran. Nucl. Sci. NS-|7 (1970) 165. 3) R. Tramell and F. J. Walter, Nucl. Instr. and Meth. 76 (1969) 317. 4) R. Henck, D. Gutknecht, P. S. Siffert, L. DeLaet and W. Schoenmackers, IEEE Trans Nucl. Sci. NS-17 (1970). 5) G. A. Armantrout, UCRL-71508 (1969). 6) M. Slapa, G.C. Huth, W. Seibt, M. Schieber and P.J. Randtke, IEEE Trans. Nucl. Sci. NS-23 (1976) 102. 7) L. L. Makovski, N. B. Strokam and N. I. Tisnek, Sov. Phys Semicond. 3 (1970) 928. 8) I. Beinglass, G. Dishon, A. Holzer and M. Schieber, J. Cryst. Growth 42 (1977) 166. 9) M. Schieber, 1. Beinglass, G. Dishon and A. Holzer, in Crystal Growth and Mat. Proc. First European Conf. on Crystal growth, eds., S.E. Kaldis and H.J. Scheel (North-Holland, Amsterdam, 1977)p. 279. L0) M. Schieber, W. F. Schnepple and L. Van Den Berg, J. Cryst. Growth 33 (1976) 145. II) H.R. Zulliger and D.W. Aitken, IEEE Trans. Nucl. Sci. NS-17 (1970). 12) A.J. Dabrowski and G.C. Huth, IEEE Trans. Nucl. Sci. NS-25 (1978) 205. 13) 1. Beinglass, G. Dishon, A. Holzer, S. Ofer and M. Schieber, Appl. Phys. Lett. 30 (1977) 611.