Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data
Monte-Carlo method is used for investigating the energy dependence of sensitivity of CdZnTe- and TlBr-detectors of gamma-radiation, which operate in the mode of pulse-amplitude analysis. We researched the approximate formulae that describe this dependence in the range of gamma-quantum energies from...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data / A.I. Skrypnyk // Вопросы атомной науки и техники. — 2014. — № 5. — С. 177-183. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-804812015-04-19T03:02:47Z Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data Skrypnyk, A.I. Вычислительные и модельные системы Monte-Carlo method is used for investigating the energy dependence of sensitivity of CdZnTe- and TlBr-detectors of gamma-radiation, which operate in the mode of pulse-amplitude analysis. We researched the approximate formulae that describe this dependence in the range of gamma-quantum energies from 30 keV to 3 MeV. It is proposed a method for determining the tting parameters for approximate formulae through gamma-radiation spectra measured experimentally by several reference sources of gamma-radiation. In particular, it can be ²⁴¹Am, ¹³⁷Cs and ⁶⁰Co gamma-radiation sources. It is also discussed the measurements with additional radiation sources that can be used for improving an accuracy of reconstruction of energy dependence of detectors' sensitivity. Метод Монте-Карло использован для исследования энергетической зависимости чувствительности CdZnTe- и TlBr-детекторов гамма-излучения, которые работают в режиме анализа амплитуд импульсов. Мы изучили приближенные формулы, описывающие эту зависимость в диапазоне энергий гамма-квантов от 30 кэВ до 3 МэВ. Предлагается метод определения параметров подгонки для приближенных формул по спектрам гамма-излучения, которые экспериментально измерены с помощью нескольких стандартных источников излучения. В частности, это могут быть источники гамма-излучения ²⁴¹Am, ¹³⁷Cs и ⁶⁰Co . Обсуждаются также измерения с дополнительными источниками излучений, которые могут быть использованы для улучшения точности восстановления энергетической зависимости чувствительности детекторов. Метод Монте-Карло використаний для дослiдження енергетичної залежностi чутливостi CdZnTe- i TlBr-детекторiв гамма-випромiнювання, котрi працюють в режимi аналiзу амплiтуд iмпульсiв. Ми дослiдили наближенi формули, якi описують цю залежнiсть в дiапазонi енергiй гамма-квантiв вiд 30 кеВ до 3 МеВ. Пропонується метод визначення параметрiв пiдгонки для наближених формул за спектрами гамма-випромiнювання, якi експериментально вимiрянi за допомогою декiлькох стандартних джерел випромiнювання. Зокрема, це можуть бути джерела гамма-випромiнювання ²⁴¹Am, ¹³⁷Cs та ⁶⁰Co. Обговорюються також вимiрювання з додатковими джерелами випромiнювань, якi можуть бути використанi для полiпшення точностi вiдновлення енергетичної залежностi чутливостi детекторiв. 2014 Article Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data / A.I. Skrypnyk // Вопросы атомной науки и техники. — 2014. — № 5. — С. 177-183. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 29.40.Wk, 85.30De, 07.85.-m http://dspace.nbuv.gov.ua/handle/123456789/80481 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Вычислительные и модельные системы Вычислительные и модельные системы |
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Вычислительные и модельные системы Вычислительные и модельные системы Skrypnyk, A.I. Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data Вопросы атомной науки и техники |
| description |
Monte-Carlo method is used for investigating the energy dependence of sensitivity of CdZnTe- and TlBr-detectors of gamma-radiation, which operate in the mode of pulse-amplitude analysis. We researched the approximate formulae that describe this dependence in the range of gamma-quantum energies from 30 keV to 3 MeV. It is proposed a method for determining the tting parameters for approximate formulae through gamma-radiation spectra measured experimentally by several reference sources of gamma-radiation. In particular, it can be ²⁴¹Am, ¹³⁷Cs and ⁶⁰Co gamma-radiation sources. It is also discussed the measurements with additional radiation sources that can be used for improving an accuracy of reconstruction of energy dependence of detectors' sensitivity. |
| format |
Article |
| author |
Skrypnyk, A.I. |
| author_facet |
Skrypnyk, A.I. |
| author_sort |
Skrypnyk, A.I. |
| title |
Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data |
| title_short |
Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data |
| title_full |
Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data |
| title_fullStr |
Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data |
| title_full_unstemmed |
Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data |
| title_sort |
reconstruction of energy dependence of the sensitivity of cdznte- and tlbr-detectors through the restricted data |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2014 |
| topic_facet |
Вычислительные и модельные системы |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/80481 |
| citation_txt |
Reconstruction of energy dependence of the sensitivity of CdZnTe- and TlBr-detectors through the restricted data / A.I. Skrypnyk // Вопросы атомной науки и техники. — 2014. — № 5. — С. 177-183. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT skrypnykai reconstructionofenergydependenceofthesensitivityofcdznteandtlbrdetectorsthroughtherestricteddata |
| first_indexed |
2025-07-06T04:29:38Z |
| last_indexed |
2025-07-06T04:29:38Z |
| _version_ |
1836870458664812544 |
| fulltext |
RECONSTRUCTION OF ENERGY DEPENDENCE OF THE
SENSITIVITY OF CdZnTe- AND TlBr-DETECTORS
THROUGH THE RESTRICTED DATA
A. I. Skrypnyk∗
National Science Center ”Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine
(Received June 24, 2014)
Monte-Carlo method is used for investigating the energy dependence of sensitivity of CdZnTe- and TlBr-detectors of
gamma-radiation, which operate in the mode of pulse-amplitude analysis. We researched the approximate formulae
that describe this dependence in the range of gamma-quantum energies from 30 keV to 3 MeV. It is proposed a
method for determining the fitting parameters for approximate formulae through gamma-radiation spectra measured
experimentally by several reference sources of gamma-radiation. In particular, it can be 241Am, 137Cs and 60Co
gamma-radiation sources. It is also discussed the measurements with additional radiation sources that can be used
for improving an accuracy of reconstruction of energy dependence of detectors’ sensitivity.
PACS: 29.40.Wk, 85.30De, 07.85.-m
1. INTRODUCTION
The study of wide-band gap semiconductor radi-
ation detectors is of great interest for far more than
one year. Cd(Zn)Te-, TlBr-, HgI2-materials are ones
of the most suitable candidates for creating commer-
cially available radiation detection systems with quite
good spectroscopic properties in the cases of opera-
ting at room temperatures [1, 2]. However, some fea-
tures of these semiconductor materials create prob-
lems in determining a detector’s main operating char-
acteristics such as the dependence of their sensitivity,
δ, on the energy of the detected gamma-rays. The va-
riety of electrophysical characteristics of wide-band
gap semiconductor detectors results in the signifi-
cant variations in the sensitivity of identical detectors
working under the same bias condition. It causes a
necessity of detailed measurements of energy depen-
dence of the sensitivity for every detector.
Considerable assistance in answering these prob-
lems may spring from first principles’ simulations of
material and detector operation. It could be of help in
developing semi-experimental methods for estimating
and measuring detector parameters, such as the ener-
gy dependence of the detectors’ sensitivity. Simu-
lation will be especially useful for multi-detector sys-
tems wherein the sensitivity of all components must
be known and taken into account for optimal system
performance.
In the present work, simulation of response of
CdZnTe- and TlBr-detectors was researched. Analy-
sis of energy dependence of detectors’ sensitivity was
made. It was considered the simple approximation
formulae for determining the dependence of the sen-
sitivity for CdZnTe- and TlBr-detectors on the energy
for gamma-rays in the energy range from 30 keV to
3MeV. Fitting parameters for these formulae can be
determined with a satisfactory accuracy basing on the
measurements of gamma-quantum spectra from sev-
eral reference sources. Analysis of results from sim-
ulation of response functions and energy dependence
of sensitivity for CdZnTe-detectors allowed to pro-
pose a method for calculating the fitting parameters
of approximate formulae based on the experimentally
measured gamma-ray spectra from 241Am, 137Cs and
60Co reference sources. This method was used for re-
constructing the energy dependence of sensitivity of
CdZnTe-detector. Numerical experiment allowed us
to confirm a validity of the obtained approximate for-
mulae for TlBr-detectors. Overall, it was concluded
that the sensitivity of CdZnTe- and TlBr-detectors
can be adequately reconstructed using approximation
formulae which, therefore, appreciably simplify the
procedures of their calibration.
2. MODEL VERIFICATION
To investigate characteristics of TlBr- and
CdZnTe-detectors Geant4 v.4.9.6 package – univer-
sal toolkit for the simulating the passage of charged
particles, neutrons and gamma-quanta through mat-
ter [3] was used. We simulated the passage of
gamma-quanta through the detectors by Monte-Carlo
method via the user program code described detail in
[4], embedded in Geant4-package.
The user program code mimics the detector’s res-
ponse for every gamma-quantum. Firstly, program
calculates the value of the ionization energy, Ei,
∗Corresponding author E-mail address: belkas@kipt.kharkov.ua
ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2014, N5 (93).
Series: Nuclear Physics Investigations (63), p.177-183.
177
transferred to the detector by the absorbed gamma-
quantum with the initial energy of Eγ, and, secondly,
it computers the value of charge induced on the de-
tector’s contacts for every interacted photon.
To obtain from Monte-Carlo simulation the detec-
tor’s response function that will be in a good agree-
ment with the experimental response function of real
detector the user program code takes into account the
great number of factors which influence on the am-
plitude of the induced charge including fluctuations
in the generation of electron-hole pairs, variations in
the numbers of collected electrons and holes and elec-
tronic noise [4].
Previously, for calculating the response functions
of CdTe- and Cd(Zn)Te-detectors with this model,
the EGSnrc Monte-Carlo code was used. In [5, 6]
we compared results of Monte-Carlo simulation ob-
tained by EGSnrc- and Geant4-packages. We ob-
tained a good agreement between calculated- and
experimental-data for gamma-ray lines that can be
considered almost monochromatic.
3. DETERMINATION OF ENERGY
DEPENDENCE OF TlBr- AND
CdZnTe-DETECTORS’ SENSITIVITY
One of the critical characteristics that determines
the operating the semiconductor gamma-radiation
detectors at room temperatures is their sensitivity, δ,
that is defined as the ratio of the number of pulses,
N, produced by the detector to the value of exposure
(X) or absorbed (D) radiation dose: δX = N/X or
δD = N/D. A sharp dependency of sensitivity from
the gamma-radiation energy, δX,D(Eγ), is a charac-
teristic feature of all wide band-gap semiconductors
used for detecting gamma-quanta.
The measurement of sensitivity of detectors is a
laborious problem. To determine this value for semi-
conductor detectors in the range of gamma-quantum
energies from 30 keV to 3MeV it is necessary about
10 reference gamma-radiation sources. In some cases,
it is not possible to conduct experiment with such
number of reference sources. Monte-Carlo simulation
of semiconductor detectors can be used as solution
of this problem. However, for obtaining correct va-
lues of sensitivity via Monte-Carlo simulation it needs
to have accurate characteristics of detectors some of
which, for example, electrophysical parameters, are
not always known.
Analytic formulae exist for only the simplest ge-
ometries of measurement setup in which the influence
of the Compton scattering of gamma-rays is negli-
gible. In such cases, the user can easily calculate
the radiation dose created by the gamma-quantum
flow. The principal reason is that the Compton scat-
tering changes the energy spectrum of gamma-rays
in a manner that is highly dependent on the detec-
tor dimensions. It does not allow to obtain analyti-
cal expressions for calculating the energy dependence
of sensitivity of semiconductor detectors in the wide
range of energies of gamma-quanta.
In the present work, we used Monte-Carlo
method for simulating the response functions of two
types of planar semiconductor detectors of gamma-
radiation: CdZnTe and TlBr. Firstly, we consid-
ered 6 × 6 × 3 mm3 CdZnTe-detector. Fig. 1
plots δX(Eγ), the energy dependency of sensitivity
of such detector, calculated by the Geant4 code at
a zero-noise discrimination threshold. At gamma-
ray energies between 10 and 60 keV the sensitiv-
ity, δX(Eγ), increases by more than one order-of-
magnitude. In contrast, at gamma-ray energies bet-
ween 80 keV and 1MeV, the sensitivity drops by more
than two orders of magnitude. An analytical form
for the energy dependency, δX(Eγ), in the entire
range of gamma-quantum energies between 10 keV
and 3MeV cannot be obtained. Thus, the curve
of sensitivity was divided into 3 parts. The behav-
ior of δX(Eγ) in CdZnTe-detectors in the different
energy ranges was approximated by three different
functions. In Fig.1 and the following ones, the names
of fitting functions correspond to the names that are
used in the Origin 9 software [7]. The log-log scale of
Fig.1 specifies the visible shape of the fitting curves.
0.01 0.1 1
102
103
104
3
2
Geant4
1) Linear fit
2) Holliday fit
3) Reciprocal fit
E , MeV
1
X, pulse/ R
Fig.1. Approximate description of the dependency,
δX(Eγ), in three ranges of gamma-ray energies
It is easy to determine an analytical form of func-
tions that approximates a dependency of δX(Eγ) in
regions 1 and 3. At gamma-ray energies between 10
and 60 keV (region 1), the sensitivity of the CdZnTe-
detector can be approximated by a linear function
such as
δX(Eγ) ≈ a1 + b1 × Eγ , Eγ < 60 keV. (1)
At gamma-quantum energies more than 0.3MeV (re-
gion 3), the inverse dependency is evident in the form
δX(Eγ) ≈
1
a3 + b3 × Eγ
, Eγ > 0.3MeV. (2)
In Eqs. (1) and (2), the values of a1, b1, a3, and
b3 are the fitting parameters that can be determined
from the data of the experimental measurements of
the energy dependency, δX(Eγ). The difference be-
tween units for measuring energy (keV and MeV) in
Eqs. (1) and (2) is related to the method of deter-
mining the fitting parameters.
178
In region 1, good accuracy was achieved in eval-
uating the parameters for the linear fitting Eq. (1)
with only three experimental points. For example,
they could be measurements of δX(Eγ), the sensitiv-
ity of CdZnTe detectors, for gamma-ray energies of
31.6 keV (133Ba source, multiplet) or 32.9 keV (137Cs
source, multiplet) plus 39.9 keV (152Eu source, dou-
blet) and 59.54 keV (241Am source, monoenergetic
line). For gamma-ray energies up to approximately
80 keV, the Compton scattering in CdZnTe is in-
significant, and the probability of the photoelectric
absorption is very high. The process of reconstruct-
ing the functional dependency of δX(Eγ) and de-
termining the sensitivity of CdZnTe-detectors in the
range of gamma-ray energies between 25 and 60 keV
is sufficiently easy. Below 25 keV the results of lin-
ear fitting with only three experimental points are
doubtful in that it is apparently connected with a
near-vertical slope of the approximation curve.
The sensitivity of the investigated CdZnTe-
detectors reaches a maximum value at gamma-rays
between 60 and 80 keV. Moreover, in this energy
range, the value of sensitivity, δX(Eγ), changes only
within 5%, so for the given approximations, it is as-
sumed that it is constant. It was shown [6] that the
determination of the fitting parameters for Eq. (2)
can be simplified by rewriting it in the form
1
δX(Eγ)
≈ a3 + b3 × Eγ , Eγ > 0.3MeV. (3)
In this case, a linear function can be fitted through
three experimental points. In reconstructing the
high-energy region for the dependency of the sensitiv-
ity of CdZnTe-detectors from the gamma-ray energy,
we can use experimental data for 241Am-, 137Cs- and
60Co-sources.
In Table 1, we compare the coefficients of fitting
functions Eq. (1) and (3) obtained by analyzing an
array of values of the simulated functions, δX(Eγ),
and using only three points in regions 1 and 3 of this
function (see Fig.1).
According to the data from Table 1, the variation
in the coefficients of the slope of linear dependencies
used for approximating the energy dependency of the
sensitivity of detectors is no more than 9%. Hence,
we can, with satisfactory accuracy, reconstruct the
dependency of δX(Eγ) in regions 1 and 3 (see Fig.1)
through three measured values of sensitivity.
Table 1. Coefficients of approximation Eqs. (1) and (3) for CdZnTe detector
Approximation formula
Slope, b1,3
Ratio,
bfull/bthree
Whole array of data, bfull Three points, bthree
δX(Eγ) ≈ a1 + b1 × Eγ ,
Eγ < 60 keV
250± 10, pulse/(µR× keV ) 230± 28, pulse/(µR× keV ) 1.09
1
δX(Eγ)
≈ a3 + b3 × Eγ ,
Eγ > 0.3 MeV
0.01891± 0.00021,
µR/(MeV × pulse)
0.01869± 0.00025,
µR/(MeV × pulse)
1.01
From Fig.1 it is evident that the regions 2 and
3 of the δX(Eγ) dependency partially overlap in the
energy range from 300 to 400 keV. The analysis of
the calculated dependency of 1/δX(Eγ) showed that
in considering gamma-ray energies between approxi-
mately 0.08- and 0.4MeV, it is convenient to use the
next approximation formula with less number of fit-
ting parameters
1
δX(Eγ)
≈ a× Eb
γ , 0.08MeV < Eγ < 0.4MeV. (4)
Fig.2 demonstrates the result of using Eq. (4) for
fitting the calculated dependency of 1/δX(Eγ) in the
range of low gamma-ray energies. As illustrated, em-
ploying Eq. (4) for fitting the dependency of δX(Eγ)
through three energies is equally effective as model-
ing the sensitivity in detail by a Monte-Carlo method.
The data from Table 2 show that the difference be-
tween the coefficients of Eq. (4) obtained by approx-
imating the different sets of data is 1...3%.
In deciding on the experimental points for the
fitting, we take into account first those as follows
from the data in Fig. 1 δX(60 keV ) ≈ δX(80 keV ).
The choice of a gamma-ray energy of 122.06 keV
as the second point is conditioned by the fact that
for a 57Co source, the contribution in the measured
sensitivity of CdZnTe-detectors from this line con-
siderably exceeds the contribution from all other
high-energy lines, and the contribution in the mea-
sured sensitivity from 14.4 keV line is subtracted
easily. The quality of the fitting in the energy
range from 0.08 to 0.4MeV depends on the possi-
bility of measuring the third point. A monoenergetic
203Hg (E=279.2 keV) source is a very good candi-
179
date; however, the 203Hg isotope has a half-life of only
46.6 days. For the 51Cr isotope that also has an inten-
sive single line, E=320.1 keV, the half-life is 27.7 days.
0.0 0.1 0.2 0.3 0.4
0
1x10-3
2x10-3
3x10-3
1/ X , R/pulse
Geant4
Allometric fit
three-point fit
E , MeV
Fig.2. Fitting of the dependency of 1/δX(Eγ) of
CdZnTe-detector in the range of gamma-ray energies
between 90 and 400 keV
Table 2. Fitting parameters for Eq. (4)
Parameter
Whole array
of data
Three
points
Ratio
b 2.38± 0.05 2.4± 0.1 0.99
a 0.029±0.002 0.03±0.003 0.97
For an approximate calculation, the partial overlap-
ping in regions 2 and 3 of the energy dependency
of the sensitivity, δX(Eγ), was used. For the third
point needed to obtain an approximation in region
2, the value for δX (at 0.4 MeV) obtained by Eq. (3)
can be used. However, in this case, the discrep-
ancy in the fitting through three points with detailed
Monte-Carlo simulation may reach up to several tens
of percents. For example, for the CdZnTe-detector
we investigated, the sensitivity, δX(Eγ), obtained by
Eq. (4) for the range of gamma-quantum energies
from 0.2 to 0.4 MeV is understated by no less than
one third.
Fig.3 presents the difference between the ap-
proximate 1/δ calculation with investigated formulae
and the Monte-Carlo simulation data for CdZnTe-
detectors. It is evident that the maximum discrep-
ancy is about 10%. TlBr-detector was simulated via
Geant4 package for verification of possibility of using
the formulae investigated above for TlBr-material.
The Fig.4 shows the 1/δ dependence for
7 mm2×1 mm TlBr-detectors in the energy range Eγ
below 0.3 MeV and its fitting by the formula (4). It
is evident that sensitivity of TlBr-detectors can be
reconstructed with a good accuracy.
Fig.5 presents the total 1/δ dependence for TlBr-
detector. As we can see TlBr-detector does not have a
linear energy dependence of sensitivity in the high en-
ergy region as it was shown for CdZnTe-detector [4].
Thus, we cannot use the formula (3) for reconstruct-
ing the sensitivity in the range of gamma-quantum
energies above 0.3MeV. However, in this case we can
apply the more complicated formula, which is also
correct for CdZnTe-detector:
1
δX(Eγ)
=
a× b× E1−c
γ
1 + b× E1−c
γ
, Eγ > 0.3MeV. (5)
1 2
0
10
20
, %
E , MeV
CdZnTe
E < 0.3 MeV
E > 0.3 MeV
Fig.3. The difference between the approximate
1/δ calculation with investigated formulae and the
Monte-Carlo simulation data for CdZnTe-detectors
0.0 0.1 0.2
0
4x10-3
8x10-3
1/ , R/pulse
E , MeV
TlBr
Simulation
Formula (4)
Fig.4. The 1/δ dependence at Eγ below 0.3MeV
for TlBr-detector
0 1 2
0.0
0.2
0.4
0.6
1/ , R/pulse
E , MeV
TlBr
Simulation
Formula (5)
Fig.5. The total 1/δ dependence for TlBr-detector
The difference between the approximate 1/δ
calculation with investigated formulae and the
Monte-Carlo simulation data for TlBr-detectors is
shown in Fig.6. We can conclude that max-
imum discrepancy between values of 1/δ ob-
180
tained by formulae and simulation is in the
range about from 0.32 MeV to 0.38 MeV.
1 2
-0.2
0.0
0.2
, %
E , MeV
TlBr
E < 0,3 MeV
E > 0,3 MeV
Fig.6. The difference between the approximate
1/δ calculation with investigated formulae and the
Monte-Carlo simulation data for TlBr-detectors
Overall, the sensitivity of CdZnTe- and TlBr-
detectors can be restored by the investigated ap-
proximate formulae in the range of gamma-quantum
energies from 30 keV to 3 MeV.
4. EXAMPLE OF RECONSTRUCTING
THE SENSITIVITY OF
CdZnTe-DETECTOR THROUGH
EXPERIMENTAL DATA
Basing on data of Ref. [6] we considered the ex-
ample of reconstruction of CdZnTe-detector’s sensi-
tivity. To reconstruct the sensitivity by investigated
formulae described above it was used the experi-
mental data derived from 5×5×1.8 mm3 CdZnTe-
detector with known values of transport parame-
ters for electrons and holes. Its sensitivity was
measured in the reference points through gamma-
quantum spectra with 59.54 keV (241Am), 122.06 keV
(57Co), 661.67 keV (137Cs), and 1.28 MeV (60Co)
energies. For evaluating the spectrum of gamma-
rays from the 241Am source, the chosen discrimi-
nation threshold of noise was at a level of 40 keV.
Other spectra were obtained at the 60 keV discrim-
ination threshold for noise. The bias voltage of de-
tectors in all measurements was 300 V. In detailing
the results of fitting in Fig.7, the respective depen-
dency, δX(Eγ), obtained by simulating the response
of CdZnTe-detectors using the Geant4 toolkit was
shown.
Fig.7 reveals that the maximum difference be-
tween the function of δX(Eγ) reconstructed through
experimental measurements and data of simulation
is evident at the edges of the fitting region, i.e., in
the range of gamma-ray energies below 90 keV and
in the energy range from 0.3 to 0.5 MeV. Additional
experimental measurements of sensitivity, δX(Eγ), in
these ranges of gamma-quantum energies essentially
should improve the quality-of-fit.
In Table 3, it was compared the values of the
parameters of approximation functions for the re-
constructed dependency, δX(Eγ), and for the depen-
dency, δX(Eγ), obtained from the findings of our de-
tailed Monte-Carlo simulation. The parameters of
approximation function in region 3 agree with the
results of the simulation much better than in re-
gion 2. This may reflect the absence of the ex-
perimental measurements for the sensitivity of the
CdZnTe-detector in the range of gamma-ray energies
from 300 to 400 keV. For obtaining parameters for
the approximation function in region 2, a value of
δX(Eγ = 0.4MeV ) calculated from the approximate
dependency, δX(Eγ), in region 3 was used. The es-
sential difference between the ADC step size in the
measurements (about 0.7 keV) and for the simulation
(50 eV) of the response of CdZnTe detectors may be
another factor affecting the quality-of-fit in region 2.
It was concluded that using the presented
methodology gives satisfactory results for recon-
structing the energy dependency of the sensitivity for
CdZnTe-detectors. From the considered example we
see that this method can be applied to the cases of
high electronic noise and a lack of extensive experi-
mental data.
0.1 1
101
102
103
137Cs
60Co
57Co
E , MeV
Geant4
Fitting section 2
Fitting section 3
Experiment
X , pulse/ R
241Am
Fig.7. Example of reconstruction of dependency,
δX(Eγ), for the 5× 5× 1.8 mm3 CdZnTe detector
5. CONCLUSIONS
We investigated the dependence of energy sensi-
tivity of CdZnTe- and TlBr-detectors. The approx-
imate formulae for reconstructing the sensitivity of
CdZnTe were researched. It was shown that the
greater part of the curve of sensitivity may be re-
constructed using measurements with three reference
sources. However, presence of other measurements
can significantly improve the accuracy of reconstruc-
tion.
In region 1 (Eγ < 60 keV ) the sensitivity can
be reconstructed through three experimental refer-
ence points, such as with 137Cs (32.9 keV), 152Eu
(39.9 keV) and 241Am (59.54 keV) sources. The
reconstruction of sensitivity in region 2 (90 keV<
Eγ < 0.3 MeV) require measurements with 241Am
(59.54 keV) and 57Co (122.06 keV) sources. Also,
short-lived isotope of 203Hg (Eγ = 279.2 keV) can be
used. In region 3 (Eγ > 0.3 MeV) the energy depen-
dence of the sensitivity, δX(Eγ), for planar CdZnTe-
detectors can be reconstructed based on experimental
measurements of sensitivity also at three reference
points with 241Am (59.54 keV), 137Cs (661.67 keV),
and 60Co (about 1.28 MeV) sources.
181
Table 3. Fitting parameters for reconstructed dependency, δX(Eγ), for the 5× 5× 1.8 mm3
CdZnTe-detector
Approximation formula
Parameters
Experiment Simulation
1
δX(Eγ)
≈ a× Eb
γ ,
0.08MeV < Eγ < 0.4MeV
a = 0.19± 0.01
pulse/(µR×MeV )
b = 2.84± 0.06
a = 0.12± 0.01
pulse/(µR×MeV )
b = 2.51± 0.09
1
δX(Eγ)
≈ a3 + b3 × Eγ ,
Eγ > 0.3MeV
b3 = 0.052± 0.002
µR/(pulse×MeV )
a3 = −0.007± 0.002, µR/pulse
b3 = 0.0502± 0.0006
µR/(pulse×MeV )
a3 = −0.0081±0.0008, µR/pulse
Maximum discrepancy of 1/δ values in the total
range from 30 keV to 3 MeV obtained by the investi-
gated formulae and Monte-Carlo simulation is about
10%.
We used the investigated formula obtained for
CdZnTe-detectors for reconstructing the sensitivity
of TlBr detectors. Our analysis allows us to conclude
that more quantity of these formulae can be useful for
receiving TlBr-detectors’ sensitivity. Maximum dis-
crepancy of 1/δ values obtained by the investigated
formulae and Monte-Carlo simulation is in the range
about from 0.32 MeV to 0.38 MeV.
The energy dependence of the sensitivity for
CdZnTe-detector was reconstructed by approximate
formulae within a satisfactory accuracy through the
experimental measurements in the reference gamma-
quantum spectra with 59.54 keV (241Am), 122.06 keV
(57Co), 661.67 keV (137Cs), and 1.28 MeV (60Co) en-
ergies.
ACKNOWLEDGEMENTS
Author is very grateful to A.V. Rybka and
V.E. Kutny for providing the experimental data for
CdZnTe-detector and Prof. M.A. Khazhmuradov for
his help in the interpretation of the obtained results.
References
1. Demet Demir, Pinar Onder, Tuba Oznuluer. Per-
formance of CdTe-detector in the 13...1333 keV
energy range // Radiation Physics and Chem-
istry. 2010, v. 79, p. 1132-1136.
2. A.Churilov, et al. TlBr and TlBrxI1 − x crystals
for γ-ray detectors // Journal of Crystal Growth.
2010, v. 32, p. 1221–1227.
3. S.Agostinelli, et al. Geant4—a simulation toolkit
// Nuclear Instruments and Methods in Physics
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4. A. Zakharchenko, A.Rybka, V.Kutny,
A. Skrypnyk, M.Khazhmuradov, P. Fochuk,
A.Bolotnikov, R. James. Transport properties
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5. A. Skrypnyk, A. Zakharchenko,
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with EGSnrc for simulation of gamma-radiation
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// Problems of atomic science and technology.
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P.M.Fochuk, V.M. Sklyarchuk, A.E.Bolotnikov,
and R.B. James. The energy dependence of
the sensitivity for planar CdZnTe-gamma-ray-
detectors // Proc. of SPIE. 2013, v. 8852,
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7. OriginLab – Origin and OriginPro –
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http://www.originlab.com
182
ÂÎÑÑÒÀÍÎÂËÅÍÈÅ ÝÍÅÐÃÅÒÈ×ÅÑÊÎÉ ÇÀÂÈÑÈÌÎÑÒÈ
×ÓÂÑÒÂÈÒÅËÜÍÎÑÒÈ CdZnTe- è TlBr-ÄÅÒÅÊÒÎÐΠÏÎ ÎÃÐÀÍÈ×ÅÍÍÛÌ
ÄÀÍÍÛÌ
À.È.Ñêðûïíèê
Ìåòîä Ìîíòå-Êàðëî èñïîëüçîâàí äëÿ èññëåäîâàíèÿ ýíåðãåòè÷åñêîé çàâèñèìîñòè ÷óâñòâèòåëüíîñòè
CdZnTe- è TlBr-äåòåêòîðîâ ãàììà-èçëó÷åíèÿ, êîòîðûå ðàáîòàþò â ðåæèìå àíàëèçà àìïëèòóä èìïóëü-
ñîâ. Ìû èçó÷èëè ïðèáëèæåííûå ôîðìóëû, îïèñûâàþùèå ýòó çàâèñèìîñòü â äèàïàçîíå ýíåðãèé ãàììà-
êâàíòîâ îò 30 êýÂ äî 3 ÌýÂ. Ïðåäëàãàåòñÿ ìåòîä îïðåäåëåíèÿ ïàðàìåòðîâ ïîäãîíêè äëÿ ïðèáëèæåííûõ
ôîðìóë ïî ñïåêòðàì ãàììà-èçëó÷åíèÿ, êîòîðûå ýêñïåðèìåíòàëüíî èçìåðåíû ñ ïîìîùüþ íåñêîëüêèõ
ñòàíäàðòíûõ èñòî÷íèêîâ èçëó÷åíèÿ.  ÷àñòíîñòè, ýòî ìîãóò áûòü èñòî÷íèêè ãàììà-èçëó÷åíèÿ 241Am,
137Cs è 60Co. Îáñóæäàþòñÿ òàêæå èçìåðåíèÿ ñ äîïîëíèòåëüíûìè èñòî÷íèêàìè èçëó÷åíèé, êîòîðûå
ìîãóò áûòü èñïîëüçîâàíû äëÿ óëó÷øåíèÿ òî÷íîñòè âîññòàíîâëåíèÿ ýíåðãåòè÷åñêîé çàâèñèìîñòè ÷óâ-
ñòâèòåëüíîñòè äåòåêòîðîâ.
ÂIÄÍÎÂËÅÍÍß ÅÍÅÐÃÅÒÈ×ÍÎ� ÇÀËÅÆÍÎÑÒI ×ÓÒËÈÂÎÑÒI CdZnTe- i
TlBr-ÄÅÒÅÊÒÎÐIÂ ÇÀ ÄÎÏÎÌÎÃÎÞ ÎÁÌÅÆÅÍÈÕ ÄÀÍÈÕ
À. I.Ñêðèïíèê
Ìåòîä Ìîíòå-Êàðëî âèêîðèñòàíèé äëÿ äîñëiäæåííÿ åíåðãåòè÷íî¨ çàëåæíîñòi ÷óòëèâîñòi CdZnTe- i
TlBr-äåòåêòîðiâ ãàììà-âèïðîìiíþâàííÿ, êîòði ïðàöþþòü â ðåæèìi àíàëiçó àìïëiòóä iìïóëüñiâ. Ìè äî-
ñëiäèëè íàáëèæåíi ôîðìóëè, ÿêi îïèñóþòü öþ çàëåæíiñòü â äiàïàçîíi åíåðãié ãàììà-êâàíòiâ âiä 30 êåÂ
äî 3 ÌåÂ. Ïðîïîíó¹òüñÿ ìåòîä âèçíà÷åííÿ ïàðàìåòðiâ ïiäãîíêè äëÿ íàáëèæåíèõ ôîðìóë çà ñïåê-
òðàìè ãàììà-âèïðîìiíþâàííÿ, ÿêi åêñïåðèìåíòàëüíî âèìiðÿíi çà äîïîìîãîþ äåêiëüêîõ ñòàíäàðòíèõ
äæåðåë âèïðîìiíþâàííÿ. Çîêðåìà, öå ìîæóòü áóòè äæåðåëà ãàììà-âèïðîìiíþâàííÿ 241Am, 137Cs òà
60Co. Îáãîâîðþþòüñÿ òàêîæ âèìiðþâàííÿ ç äîäàòêîâèìè äæåðåëàìè âèïðîìiíþâàíü, ÿêi ìîæóòü áóòè
âèêîðèñòàíi äëÿ ïîëiïøåííÿ òî÷íîñòi âiäíîâëåííÿ åíåðãåòè÷íî¨ çàëåæíîñòi ÷óòëèâîñòi äåòåêòîðiâ.
183
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