- Email: [email protected]
Use of the EGS4 Monte Carlo code to evaluate the response of HgI2 and CdTe detectors for photons in the diagnostic energy range
,
YV V./11ZLV F.~
Nuclear Instruments and Methods in Physics Research A322 (1992) 591-595 North-Holland C
1i '
Sect iur,A
se f t I_ e Monte Carlo code evaluate the res a e detectors for photons i the diagnostic e r M. Conti, A. Del Guerra, D.
azzei and
se f HRI
. Russo
Univcasitu di Napoli, Dipartintento dt Scacnzc Fislche and INFN. Se zionc di Napoli, Pad. 20 MNIostra d'Oftremarc, 1-80125 Napoli, Italt
W. Bencivelli, E. Bertolucci, A.
essineo, V. Rosso and A. Stefanini
Unia -crsità di Pisa . Dipartinaeiito di Fisica and INFN, Srzione di Pisa. Via Vecchia Lia -ornesc 582 A, 1-56010 S. Piero a Cprado (PD. Italy
ZJ.
ottigli and P. Randaccio
Univcrsit ~i di Cagliari, Atituto di Fisica Slcdica and INFN, SeJonc di Cagliari, Cagliari. Ital.%
W.R. Nelson
Stanford Linear Accelerator Center, Stanford, CA 94309, USA
We present the results of the detailed simulation of the response of a HgI, crystal in terms of efficiency, energy and space resolutions versus photon energy in the diagnostic energy range 20-100 keV . Some configurations of CdTe crystals for positron emission tomography are also evaluated.
1 . Introduction The use of semiconductor detectors in radiology and nuclear medicine has become more and more relevant in recent years . This is both due to the improvements in solid state technology and in microelectronics and to the incieasing clinical requests for a higher efficiency, and a better energy and space resolution . We have evaluated the performance of this Class of detectors for specific diagnostic applications by using the EGS4 Monte Carlo code [1] . In previous publications we have reported the results of the simulation of a silicon crystal detector, equipped with microstrips for 2-D readout [2,3] and a comparative study of the performance of elemental and compound solid state crystals of possible use in X-ray digital radiography i4; . Among the various semiconductors. Hgl, has raised a lot of attention as a potential material for -y-ray detection . Computer simulations of HgI,_ detectors are already present in the literature [5,6] . In this paper we describe the detailed simulation of the response of a Hgl, crystal in terms of efficiency, energy and space resolutions versus the photon energy in the diagnostic energy range 20-100 keV . Some
evaluations of CdTc crystal configurations for positron emission tomography are also discussed .
2 . The Monte Carlo code We have used the general purpose analog Monte Carlo code EGS4 [11, implemented for this simulation . 1) a __ , _ at u -,.s C generale fc The The main aaame~ gv,eev.~a At,. GLLUIGJ lJl this l. )UC are : i) the radiation transport of electrons, positrons and photons can be simulated in any element, compound or mixture, ii) the dynamic range of charged particles goes from 10 keV to few TeV, while the dynamic range of photon energies lies between 1 keV and several TeV . The following physical processes are taken into account by the EGS4 code system : bremsstrahlung production, positron annihilation in flight and at rest . Molière multiple scattering, Möller (e - e - . e'e') and Bhabha We') +) scattering, continuous energy loss applied to charged particle tracks. pair production . Compton scattering, coherent (Rayleigh) scattering, photoelectric effect . In addition to these standard features, we have used in our code : the nonrelativistic angular distribution of photoelectrons, the PRESTA algorithm [7] for electron transport, and the l{-edge
111611-91)02/92/$05 .1111 .~-' 1992 - Elsevier Science Publishers B .V . All rights reserved
V . APPLICATIONS
M. Coati et al. / Use of the EGS4 Monte Carlo code
192
If
I
Z
n 2
,nf
W' 1 .
10
-8
0
6o 20 40 Kinetic Energy (1,-eV)
10 -0 0
100
80
II 20
~
40
171 60
80
100
Kinetic Energy (keV)
Fig. 1 . Transmission (a) and backscattering (b) spectra of 100 keV photons from a 0.3 mm thick F[912 slab .
photon transport together with a K-edge/L-edge sampling scheme, that we have specifically developed for compounds [8] . A kinetic energy cut-off of 10 key and of I keV was used for electrons and photons, respectively. 3. Results of the simulation for
91 2.
We hm studied the response of a Hgl2 slab (0.3 mm thickness) to a photon pencil beam in the energy range 20-100 key. The physical properties of the Hg1 semiconductor are shown in table 1 . Due to the low energy value (i.e. below 10 keV) th,: i .-edge of iodine was not considered in the simulation. The photon cross-section in this energy range is dominated by the photoelectric effect (i.e. fig . 2 of ref. [8]); thus one expects the K and L lines to clearly -,how up in the transmitted, backscattered and absorption spectra. Fig . I shows the results of the simulation for an incident photon beam energy (EO ) of 100 keV . The E0, EKa . EK13 and ELf;, lines are clearly evident in the transmitted (fig. la) and backscattered spectrum (fig. 1b) . A solid state detector has a certain noise level due to the electronic noise in the preamplifier-amplifier 2
Table I Physical properties of HgI,
Density Average energy for electron-hole creation Element Atomic number I{-edge [keV] Ka RVI KO [keV] L -edge [keV] L.ß, NeVI From ref. [9]. From ref. [10] .
system, to the incomplete charge collection and to the statistics of the charge generation. The statistics of the charge generation is intrinsically taken care ofby EGS4, which is an analog Monte Carlo program ; the electronic noise is easily simulated by superimposing a Gaussian noise to the number of electron-hole (e-h) pairs created by each event . An electronic noise of 200 equivalent electrons (rms) is generally achieved with standard preamplifiers. However, our experience with complex systems in operation on double-side p,-strip silicon crystals [11] suggested the use of a more conservative value, twice as high (i.e., 400 e-h pairs, rms); a Fano factor of 0.5 has been assumed . The incomplete charge collection contribution requires an estimate of the collection time distribution of the charges at the two electrodes. This can be introduced in EGS4 by simulating the electric field inside the detector, aiiid by considering the radiation transport process with an electric field h2h we have not attempted this specific simulation so far. Fig . 2 shows the distribution of e-h pairs as produced by 105 photons of 100 keV in a 0.3 mm thick H912 crystal . The various peaks correspond to the E. (En - K1~.), (Ec, - EnO ), (EO - Eßß,) absorption spectrum .
04 g/cm 3 4.2 eV Hg 80 83.10 1 70.10 ' 8166 ' 112 b 110 b
53 33.17 28.5 ' 314 a
0.
4.
8.
12.
16.
20.
No. e-h Pairs Fig. 2. Distribution of the electron-hole pairs created by 105 photons of 100 keV in a 0.3 mm thick Hg' 2 slab.
M. Conti et al. / Use of the EGS4 Monte Carlo code
593
c v
W
Q
50 100 Photon energy (keV)
Fig. 3 . Efficiency of a 0 .3 mm thick 1-Igl, slab versus photon energy. The software threshold is 2000 electrons . The statisti cal error is less than lr1c . Solid curve : our simulation : circles (and dotted curve) : EGS4 default.
In order to evaluate the efficiency, we have introduced a software threshold of five times the assumed electronic noise, i .e. 2000 equivalent e-h pairs, corresponding to an equivalent energy of 8 .4 keV . Thus, only those photons which produce a number of e-h pairs greater than 2000 are considered eligible to be detected by the HgI, crystal . Then we simply define efficiency as the ratio between the number of these photons and the number of incident photons onto the crystal . Since the charge collection process is not considered in tire simulation, this value of efficiency may be considered as an upper limit of the true efficiency of the detector . The result of the efficiency simulation is shown in fig. 3 as a function of the photon energy (solid line) . ®n the same figure we have also plotted the efficiency (circled points and dotted curve), as obtained with the standard (i .e . default) version of EGS4 code, i .e . no transport of the K-edge photon . The latter curve almost coincides with the absorption probability (1 - e - l"t ), where 1i is the total linear absorption coefficient and d is the thickness of the crystal . As expected, the major differences between the two curves are in the energy regions just above the Kand L-edges (see table 1) and are due to the escape probability of the corresponding K and L photons . The difference is 10% at most in our case (0 .3 mm thick crystal) and increases with decreasing thickness of the detector . In our simulation the energy resolution is dominated by the constant electronic noise (i .e . 400 e-h pairs rms); the simulated energy resolution at the photopeak as a function of the incident photon energy E is proportional to 1 /E, as expected (i .e . o-/E = 1 .7/E, with E in keV) .
Fig. 4 . 2-D spatial distribution for. 100 keV photons impinging onto a 0.3 mm thick Hgl, slab .
Finally, the simulated spatial resolution for a 100 keV photon pencil beam (impinging orthogonally onto the surface of the crystal) is presented in fig . 4 as a lego plot . The FWHM of the spatial resolution is compatible with 10 p .m, as expected from simple range considerations: 100 keV electrons have a range o about 20 gm in I-lgl, .
4.
91 2 response to the 24'Am spectrum
An 24iAm source is often used as a handy radioactive source for calibrating detectors it the low (10-1 2s' has keV) energy range . The decay scheme of several y lines [9] . We have simulated the response of a 0 .3 mm l-lgi, slab to the 24 'Am spectrum, retaining e only the most intense ones, as listed in table 2. distribution of electron-hole pairs is presented in fig. 5 . The two main peaks on the figure correspond to the 59.5 keV line and to a convolution of the 13 .9 . 17_8 and 20 .8 keV lines; the latter structure is only partially resolved because of the noise introduced in the simulation . The remaining 24'Am line at 26.3 keV is barely visible, due to its low branching ratio . The additional lines in the spectrum are generated by the escape of the iodine K-photons and the Hg L-photons .
Table 2 List of the most intense -y-lines from an
241Am
source
[keVJ
Energy
Absolute branching ratio
Normalized branching ratio used
13 .9 17.8 20 .8 26 .3 59 .5
0 .133 0 .193 0 .049 0 .024 0.357
0 .176 0.255 0.065 0 .032 0.472 V . APPLICATIONS
M. Coati et al. / lise of the EGS4 Monte Carlo code
>94 s Y S
1
7 1
r
e
~l
i i
> Y N
]L >V a
Y S
JC
Y h
h
-
> i
y Y
_
v.
ô.
12 .
No . e-h Pairs
16 . X10
Fib; . 5 . Distribution of e-h pairs as produced by an -; 'Am source (10*; photons).
Evaluation of CdTe crystal sitron emission tomograp y
configurations
for
Positron emis,iun i.umvgn aphy is a diagnostic technique: based on the simultaneous detection of two opposite 511 keV annihilation quanta from a ß + radioactive tracer in the human body [13]. The conventional detectors are lame diameter renal made of many hundreds of scintillators (BGO. Csl,y Nal, etc.) . The use of CdTe era-stall has been suggested [ 14] because of its hi® density (6.2 -/cm) . and~high Z value (4b-52) . . . .c recent technological improvements in the growth of CdTe crystal makes this solution highly attractive .
Table Efficiency, side contamination and cross talk probability of the CdTe array . Parameters for the simula :'_ion with the EGS4 user code iiCCDTECI : dimension of the elements of the array. ?.5 x 2.5 x 20 mm' (CdTe). 0.5 x 2 .5 x 20 mm z (Pb); Then thousand 511 keV photons incident on A or B or C along the major axis of the CdTe cell; 10 keV kinetic energy cutoff for both electrons and photons; S histories per second on a VAXStat90n 31(>fl Polition
Efficiency [ -d
Side contamination
Cross talk probability
Noise threshold (9 .4 keV)
A B C
63.2+1 .1 62.9± 1 .1 62.9+1 .1
0.02+0 .02 0.07±0 .03 0.09±0 .04
1 .2 +0 .1 1 .5 ±OZ 1 .5 ±0 .2
Low threshold (200 keV)
A B C
38.9+0 .8 38 .4±0 .8 37 .6±() .8
0.45+0 .09 ().48±0 .()9 0.53±0 .10
0 .18+0 .06 0 .24±0 .07 0 .32±0 .08
High threshold (350 keV)
A B C
18 .1+0 .6 17 .8±0 .6 17 .3±0 .6
0.26±0 .()7 0.22±0 .07 0.26±0 .07
0 .0 0 .0 0 .0
Fig . 6. Geometry used for the simulation of the response of an array of CdTe crystals to 511 keV -y-rays.
In order to keep the spatial resolution to its minimum (i .e . to the crystal size) and to reduce the double coincidence rate (i .e ., the cross talk), in a ring arrangement two adjacent counters are usually separated by a high Z absorption septum . To investigate the possible use of EGS4 to optimize the crystal-septum configuration, in terms of efficiency and cross talk probability, we have simulated an array of three 2 .5 x 2 .5 x 20 MM3 CdTe crystals separated by =a 0 .5 mm thick sheet of lead . The geometry used is illu:.tr -ßt` d in fig. 6 . The 511 keV photon pencil beam impinges p ",rpendicularly onto the centre crystal at three different positions A, B and C : at 1 .25, 0.75, and 0 .25 mm from the septum, respectively. To reject most of the photons deriving from the Compton interactions of the 511 keV photons within the biological target, it is conventional to setup a detector threshold in the range 200-350 keV . In table 3 we show the result of our simulation : the efficiency (i .e ., the fraction of incident photons producing a nummber of e-h pairs over threshold in the centre crystal), the side contamination (i .e . the fraction of incident photons producing a number of e-h pairs over threshold in one of the two side crystals), and the cross talk probability (i .e ., the fraction of incident photons producing a number of e-h pairs over threshold in both the centre crystal and one of the two side crystals) for the three positions A, B and C and for three threshold values : 9 .4 keV (i .e . 2000 equivalent e-h pairs), 200 and 350 keV .
6 . Conclusions We have shown that a Monte Carlo simulation can be of great help in evaluating and understanding the response of semiconductor crystals to low energy X-ray radiation . As specific examples w : have investigated the use of I-lgi, for digital radiography and of CdTe for positron emission tomography.
M. Conti et al. / Use of the EG.154 Monte Carlo code
References [1] W.R . Nelson, I-". Hirayama and D.W .O . Rogers, The EGS4 Code Syst -m, Stanford Linear Accelerator Center Report SLAC-265 (1985) . [2] G. Batignani, E. Bertolucci, U. Bottigli et ai ., Plays . Mied . 6(1990)39. [3] W. Bencivelli, E. Bertolucci, U. Bottigli et al ., Nucl. Instr. and Meth . A305 (1991) 574. [4] W. Bencivelli, E. Bertolucci, U. Bottigli et al ., Nuci . Instr. and Meth . A310 (1991) 210. [5] C. Manfredotti and U. Nastasi, Nucl . Instr. and Meth . 225 (1984) 138. [6] P. Olmos, J.M . Perez, G. Garcia-Belmonte, A. Bru and J.L . de Pablos, Nucl . Instr. and Meth . A302 (1991) 91 . [7] A.F . Bielajew and D.W .O . Rogers, Nucl . Instr. and Meth . B18 (1991) 165.
595
[8] A. Del Guerra, W.R . Nelson and P. Russo, Nucl . Instr.
and Meth . A306 (1991) 378. [9] C.M . Lederer and V.S. Shirley (eds .), Table of Isotopes, 7th edition (Wiley, New York. 1978) appendix 11, p. 4. [10] E. Storm and H.I. Israel, Atom . Data Nucl . Data Tables 7 (1970) 565. [11] B. Alfano, A. Bandettini, W. Bencivelli et al ., Phys . Med. Biol . 37 (1992) 1167. [12] A.F. Bielajew, in: Monte Carlo Transport of Electrons and Photons, eds. T.M . Jenkins, W.R . Nelson and A. Rindi, E. Majorana International Science Series (Plenum, New York, 1988) p. 421 . [13] See, e.g .: A. Del Guerra, Physica Scripta T-19 (1987) 481 . [14] G. Baldazzi, D. Bollini, F. Casali et al., in : Atti del Convegno Nazionale di Fisica Biomedica, ed . S. Lazzeri, Cesena, Italy, December 13-14, 1990. pp . 87-97.
V. APPLICATIONS
YV V./11ZLV F.~
Nuclear Instruments and Methods in Physics Research A322 (1992) 591-595 North-Holland C
1i '
Sect iur,A
se f t I_ e Monte Carlo code evaluate the res a e detectors for photons i the diagnostic e r M. Conti, A. Del Guerra, D.
azzei and
se f HRI
. Russo
Univcasitu di Napoli, Dipartintento dt Scacnzc Fislche and INFN. Se zionc di Napoli, Pad. 20 MNIostra d'Oftremarc, 1-80125 Napoli, Italt
W. Bencivelli, E. Bertolucci, A.
essineo, V. Rosso and A. Stefanini
Unia -crsità di Pisa . Dipartinaeiito di Fisica and INFN, Srzione di Pisa. Via Vecchia Lia -ornesc 582 A, 1-56010 S. Piero a Cprado (PD. Italy
ZJ.
ottigli and P. Randaccio
Univcrsit ~i di Cagliari, Atituto di Fisica Slcdica and INFN, SeJonc di Cagliari, Cagliari. Ital.%
W.R. Nelson
Stanford Linear Accelerator Center, Stanford, CA 94309, USA
We present the results of the detailed simulation of the response of a HgI, crystal in terms of efficiency, energy and space resolutions versus photon energy in the diagnostic energy range 20-100 keV . Some configurations of CdTe crystals for positron emission tomography are also evaluated.
1 . Introduction The use of semiconductor detectors in radiology and nuclear medicine has become more and more relevant in recent years . This is both due to the improvements in solid state technology and in microelectronics and to the incieasing clinical requests for a higher efficiency, and a better energy and space resolution . We have evaluated the performance of this Class of detectors for specific diagnostic applications by using the EGS4 Monte Carlo code [1] . In previous publications we have reported the results of the simulation of a silicon crystal detector, equipped with microstrips for 2-D readout [2,3] and a comparative study of the performance of elemental and compound solid state crystals of possible use in X-ray digital radiography i4; . Among the various semiconductors. Hgl, has raised a lot of attention as a potential material for -y-ray detection . Computer simulations of HgI,_ detectors are already present in the literature [5,6] . In this paper we describe the detailed simulation of the response of a Hgl, crystal in terms of efficiency, energy and space resolutions versus the photon energy in the diagnostic energy range 20-100 keV . Some
evaluations of CdTc crystal configurations for positron emission tomography are also discussed .
2 . The Monte Carlo code We have used the general purpose analog Monte Carlo code EGS4 [11, implemented for this simulation . 1) a __ , _ at u -,.s C generale fc The The main aaame~ gv,eev.~a At,. GLLUIGJ lJl this l. )UC are : i) the radiation transport of electrons, positrons and photons can be simulated in any element, compound or mixture, ii) the dynamic range of charged particles goes from 10 keV to few TeV, while the dynamic range of photon energies lies between 1 keV and several TeV . The following physical processes are taken into account by the EGS4 code system : bremsstrahlung production, positron annihilation in flight and at rest . Molière multiple scattering, Möller (e - e - . e'e') and Bhabha We') +) scattering, continuous energy loss applied to charged particle tracks. pair production . Compton scattering, coherent (Rayleigh) scattering, photoelectric effect . In addition to these standard features, we have used in our code : the nonrelativistic angular distribution of photoelectrons, the PRESTA algorithm [7] for electron transport, and the l{-edge
111611-91)02/92/$05 .1111 .~-' 1992 - Elsevier Science Publishers B .V . All rights reserved
V . APPLICATIONS
M. Coati et al. / Use of the EGS4 Monte Carlo code
192
If
I
Z
n 2
,nf
W' 1 .
10
-8
0
6o 20 40 Kinetic Energy (1,-eV)
10 -0 0
100
80
II 20
~
40
171 60
80
100
Kinetic Energy (keV)
Fig. 1 . Transmission (a) and backscattering (b) spectra of 100 keV photons from a 0.3 mm thick F[912 slab .
photon transport together with a K-edge/L-edge sampling scheme, that we have specifically developed for compounds [8] . A kinetic energy cut-off of 10 key and of I keV was used for electrons and photons, respectively. 3. Results of the simulation for
91 2.
We hm studied the response of a Hgl2 slab (0.3 mm thickness) to a photon pencil beam in the energy range 20-100 key. The physical properties of the Hg1 semiconductor are shown in table 1 . Due to the low energy value (i.e. below 10 keV) th,: i .-edge of iodine was not considered in the simulation. The photon cross-section in this energy range is dominated by the photoelectric effect (i.e. fig . 2 of ref. [8]); thus one expects the K and L lines to clearly -,how up in the transmitted, backscattered and absorption spectra. Fig . I shows the results of the simulation for an incident photon beam energy (EO ) of 100 keV . The E0, EKa . EK13 and ELf;, lines are clearly evident in the transmitted (fig. la) and backscattered spectrum (fig. 1b) . A solid state detector has a certain noise level due to the electronic noise in the preamplifier-amplifier 2
Table I Physical properties of HgI,
Density Average energy for electron-hole creation Element Atomic number I{-edge [keV] Ka RVI KO [keV] L -edge [keV] L.ß, NeVI From ref. [9]. From ref. [10] .
system, to the incomplete charge collection and to the statistics of the charge generation. The statistics of the charge generation is intrinsically taken care ofby EGS4, which is an analog Monte Carlo program ; the electronic noise is easily simulated by superimposing a Gaussian noise to the number of electron-hole (e-h) pairs created by each event . An electronic noise of 200 equivalent electrons (rms) is generally achieved with standard preamplifiers. However, our experience with complex systems in operation on double-side p,-strip silicon crystals [11] suggested the use of a more conservative value, twice as high (i.e., 400 e-h pairs, rms); a Fano factor of 0.5 has been assumed . The incomplete charge collection contribution requires an estimate of the collection time distribution of the charges at the two electrodes. This can be introduced in EGS4 by simulating the electric field inside the detector, aiiid by considering the radiation transport process with an electric field h2h we have not attempted this specific simulation so far. Fig . 2 shows the distribution of e-h pairs as produced by 105 photons of 100 keV in a 0.3 mm thick H912 crystal . The various peaks correspond to the E. (En - K1~.), (Ec, - EnO ), (EO - Eßß,) absorption spectrum .
04 g/cm 3 4.2 eV Hg 80 83.10 1 70.10 ' 8166 ' 112 b 110 b
53 33.17 28.5 ' 314 a
0.
4.
8.
12.
16.
20.
No. e-h Pairs Fig. 2. Distribution of the electron-hole pairs created by 105 photons of 100 keV in a 0.3 mm thick Hg' 2 slab.
M. Conti et al. / Use of the EGS4 Monte Carlo code
593
c v
W
Q
50 100 Photon energy (keV)
Fig. 3 . Efficiency of a 0 .3 mm thick 1-Igl, slab versus photon energy. The software threshold is 2000 electrons . The statisti cal error is less than lr1c . Solid curve : our simulation : circles (and dotted curve) : EGS4 default.
In order to evaluate the efficiency, we have introduced a software threshold of five times the assumed electronic noise, i .e. 2000 equivalent e-h pairs, corresponding to an equivalent energy of 8 .4 keV . Thus, only those photons which produce a number of e-h pairs greater than 2000 are considered eligible to be detected by the HgI, crystal . Then we simply define efficiency as the ratio between the number of these photons and the number of incident photons onto the crystal . Since the charge collection process is not considered in tire simulation, this value of efficiency may be considered as an upper limit of the true efficiency of the detector . The result of the efficiency simulation is shown in fig. 3 as a function of the photon energy (solid line) . ®n the same figure we have also plotted the efficiency (circled points and dotted curve), as obtained with the standard (i .e . default) version of EGS4 code, i .e . no transport of the K-edge photon . The latter curve almost coincides with the absorption probability (1 - e - l"t ), where 1i is the total linear absorption coefficient and d is the thickness of the crystal . As expected, the major differences between the two curves are in the energy regions just above the Kand L-edges (see table 1) and are due to the escape probability of the corresponding K and L photons . The difference is 10% at most in our case (0 .3 mm thick crystal) and increases with decreasing thickness of the detector . In our simulation the energy resolution is dominated by the constant electronic noise (i .e . 400 e-h pairs rms); the simulated energy resolution at the photopeak as a function of the incident photon energy E is proportional to 1 /E, as expected (i .e . o-/E = 1 .7/E, with E in keV) .
Fig. 4 . 2-D spatial distribution for. 100 keV photons impinging onto a 0.3 mm thick Hgl, slab .
Finally, the simulated spatial resolution for a 100 keV photon pencil beam (impinging orthogonally onto the surface of the crystal) is presented in fig . 4 as a lego plot . The FWHM of the spatial resolution is compatible with 10 p .m, as expected from simple range considerations: 100 keV electrons have a range o about 20 gm in I-lgl, .
4.
91 2 response to the 24'Am spectrum
An 24iAm source is often used as a handy radioactive source for calibrating detectors it the low (10-1 2s' has keV) energy range . The decay scheme of several y lines [9] . We have simulated the response of a 0 .3 mm l-lgi, slab to the 24 'Am spectrum, retaining e only the most intense ones, as listed in table 2. distribution of electron-hole pairs is presented in fig. 5 . The two main peaks on the figure correspond to the 59.5 keV line and to a convolution of the 13 .9 . 17_8 and 20 .8 keV lines; the latter structure is only partially resolved because of the noise introduced in the simulation . The remaining 24'Am line at 26.3 keV is barely visible, due to its low branching ratio . The additional lines in the spectrum are generated by the escape of the iodine K-photons and the Hg L-photons .
Table 2 List of the most intense -y-lines from an
241Am
source
[keVJ
Energy
Absolute branching ratio
Normalized branching ratio used
13 .9 17.8 20 .8 26 .3 59 .5
0 .133 0 .193 0 .049 0 .024 0.357
0 .176 0.255 0.065 0 .032 0.472 V . APPLICATIONS
M. Coati et al. / lise of the EGS4 Monte Carlo code
>94 s Y S
1
7 1
r
e
~l
i i
> Y N
]L >V a
Y S
JC
Y h
h
-
> i
y Y
_
v.
ô.
12 .
No . e-h Pairs
16 . X10
Fib; . 5 . Distribution of e-h pairs as produced by an -; 'Am source (10*; photons).
Evaluation of CdTe crystal sitron emission tomograp y
configurations
for
Positron emis,iun i.umvgn aphy is a diagnostic technique: based on the simultaneous detection of two opposite 511 keV annihilation quanta from a ß + radioactive tracer in the human body [13]. The conventional detectors are lame diameter renal made of many hundreds of scintillators (BGO. Csl,y Nal, etc.) . The use of CdTe era-stall has been suggested [ 14] because of its hi® density (6.2 -/cm) . and~high Z value (4b-52) . . . .c recent technological improvements in the growth of CdTe crystal makes this solution highly attractive .
Table Efficiency, side contamination and cross talk probability of the CdTe array . Parameters for the simula :'_ion with the EGS4 user code iiCCDTECI : dimension of the elements of the array. ?.5 x 2.5 x 20 mm' (CdTe). 0.5 x 2 .5 x 20 mm z (Pb); Then thousand 511 keV photons incident on A or B or C along the major axis of the CdTe cell; 10 keV kinetic energy cutoff for both electrons and photons; S histories per second on a VAXStat90n 31(>fl Polition
Efficiency [ -d
Side contamination
Cross talk probability
Noise threshold (9 .4 keV)
A B C
63.2+1 .1 62.9± 1 .1 62.9+1 .1
0.02+0 .02 0.07±0 .03 0.09±0 .04
1 .2 +0 .1 1 .5 ±OZ 1 .5 ±0 .2
Low threshold (200 keV)
A B C
38.9+0 .8 38 .4±0 .8 37 .6±() .8
0.45+0 .09 ().48±0 .()9 0.53±0 .10
0 .18+0 .06 0 .24±0 .07 0 .32±0 .08
High threshold (350 keV)
A B C
18 .1+0 .6 17 .8±0 .6 17 .3±0 .6
0.26±0 .()7 0.22±0 .07 0.26±0 .07
0 .0 0 .0 0 .0
Fig . 6. Geometry used for the simulation of the response of an array of CdTe crystals to 511 keV -y-rays.
In order to keep the spatial resolution to its minimum (i .e . to the crystal size) and to reduce the double coincidence rate (i .e ., the cross talk), in a ring arrangement two adjacent counters are usually separated by a high Z absorption septum . To investigate the possible use of EGS4 to optimize the crystal-septum configuration, in terms of efficiency and cross talk probability, we have simulated an array of three 2 .5 x 2 .5 x 20 MM3 CdTe crystals separated by =a 0 .5 mm thick sheet of lead . The geometry used is illu:.tr -ßt` d in fig. 6 . The 511 keV photon pencil beam impinges p ",rpendicularly onto the centre crystal at three different positions A, B and C : at 1 .25, 0.75, and 0 .25 mm from the septum, respectively. To reject most of the photons deriving from the Compton interactions of the 511 keV photons within the biological target, it is conventional to setup a detector threshold in the range 200-350 keV . In table 3 we show the result of our simulation : the efficiency (i .e ., the fraction of incident photons producing a nummber of e-h pairs over threshold in the centre crystal), the side contamination (i .e . the fraction of incident photons producing a number of e-h pairs over threshold in one of the two side crystals), and the cross talk probability (i .e ., the fraction of incident photons producing a number of e-h pairs over threshold in both the centre crystal and one of the two side crystals) for the three positions A, B and C and for three threshold values : 9 .4 keV (i .e . 2000 equivalent e-h pairs), 200 and 350 keV .
6 . Conclusions We have shown that a Monte Carlo simulation can be of great help in evaluating and understanding the response of semiconductor crystals to low energy X-ray radiation . As specific examples w : have investigated the use of I-lgi, for digital radiography and of CdTe for positron emission tomography.
M. Conti et al. / Use of the EG.154 Monte Carlo code
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[8] A. Del Guerra, W.R . Nelson and P. Russo, Nucl . Instr.
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V. APPLICATIONS