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Efficiency calibration of a Si(Li) detector in the low-energy region using electron bremsstrahlung
NUCLEAR INSTRUMENTS &METNoDS IN PHYSICS RESEARCH Nuclear
ELSEVIER
Instruments
and Methods
in Physics
Research
SecttonA
A 400 (1997) 387-391
Efficiency calibration of a Si(Li) detector in the low-energy region using electron bremsstrahlung J. Tschischgale, D. Kichler, Technische
U. Lehnert, G. Zschornack”
UniversitZit Dresden, FR Physik, Institut fiir Kern- und Teilchenphysik, Received
10 February
MommsenstraJe
13, D-01062 Dresden, Germanv
1997; received in revised form 18 June 1997
Abstract
In the low-energy region the determination of the detector efficiency is complicated by the fact of nonavailability of certificated calibration sources. To solve this problem the use of electron bremsstrahlung for determining the relative photon detection efficiency of a Si(Li) detector in the low-energy range OS-19 keV is proposed. The calibration is based on energy dispersive measurements of electron bremsstrahlung emitted by an X-ray tube. Model spectra are computed from thick-target bremsstrahlung spectra in a semiclassical approximation and from a physical model for the detector response. Model spectra are fitted to the measured spectra using a parametric adaptor term. Thereby, the error of the determined detector efficiency is approximately 5%.
1. Introduction
Efficiency calibrations of Si(Li) detectors at photon energies below 5 keV are still of great interest for a wide field of applications, but the lack of radionuclide standards in this energy range is a serious problem. For higher energies in the energy range above 5 keV a manifold of calibration sources with well-known photon energies and certificated activities are known. In recent years, the importance of the determination of the spectral quantum detection efficiency E increases because of the development of low-noise analog electronics and new types of entrance windows in the soft X-ray region. Thus, different ap-
*Corresponding
author
0168-9002/97/$17.00 (0 1997 Elsevier Science B.V. All rights reserved PII SO1 68-9002(97)00958-3
proaches have been made to solve the problem by preparing fluorescence sources, which are calibrated by using proportional counters [l] or PIXE cross-sections as in Ref. [2]. Other ways are the use of synchrotron radiation from an electron storage ring as a primary standard source [3,4] and the use of a commercially available fluorescence X-ray source in connection with measurements at several energies, above and below the Si K absorption edge, and at several X-ray beam incidence angles
L-51. An alternative method to solve the above-mentioned problem is the spectrometry of electron bremsstrahlung spectra and the subsequent deconvolution of the detector efficiency using known electron bremsstrahlung cross-sections. Thus, we have calibrated a Si(Li) detector in the energy region from 0.5 keV to 19 keV with the electron
388
J. Tschischgale et al./Nucl. lnstr. and Meth. in Phys. Res. A 400 (1997) 387-391
bremsstrahlung emitted by an X-ray tube. In this way, the course of the detector efficiency was determined independent of calibration sources emitting discrete X-ray or y lines and without using big basic machines like electron storage rings.
deeper the electron moves into the thick target. Thus, the intensity of a thick-target spectrum becomes -z/3 1,
-
~~213
~
! 2. Calculation spectra
of thick-target
(I+
bremsstrahlung
A semiclassical approximation for the description of continuous thick-target electron bremsstrahlung spectra was developed by Kramers [6] and Wentzel [7]. Wentzel calculated the bremsstrahlung spectrum, analysing the classical electron-nucleus interaction and introducing quantum mechanics by the Bohr correspondence principle. Thereby, it is assumed that an incident electron is accelerated by high voltage and the maximum frequency of an emitted photon may only be vo=-,
eU h
(1)
the so-called Duane-Hunt limit. At very low electron energies electronelectron collisions predominate, but the emitted electron bremsstrahlung is of very low energy. At higher energies the bremsstrahlung is caused by the deflection (deceleration) of the incident electron in the Coulomb field of a nucleus. Thereby, the electron will describe a hyperbolic orbit, e.g:this deflection in the Coulomb field of the nucleus will always be an accelerated motion and radiation will be emitted. The intensity radiated by an electron is characterised by the Poynting vector which is determined by the motion of the electron. Thus, the total energy loss can be found by integrating the Poynting vector over time. To obtain the spectral distribution, the electromagnetic radiation is expressed in terms of the dipole momentum of an electron harmonically oscillating about some point. Following Wentzel, the Fourier integral of frequencies for the motion along the hyperbola correspond to the frequencies of emitted radiation. After calculating the mean of all possible hyperbolas, we have to take into account that the electron has lost some energy, so that, as the maximal frequency decreases, the
0.2lS(Zfi(f&
-+=J3)),
(2)
where I, is the intensity radiated in v . v + dv, v. the maximum frequency, v the frequency, Z the atomic number and R the Rydberg constant. In the discussed case, the proportionality shown in Eq. (2) is sufficient to calculate the relative detector efficiency behaviour. For more detailed information on deducing the Wentzel formula see Ref. [7]. For higher energies, this formula is in agreement with Kulenkampff’s [8] empirical equation 1s - Z((v, - v) + aZ).
(3)
A comparison of results from Eq. (2) and the Kuhlenkampff’s formula is given in Fig. 1. As the better based physical description we use in our calculations results of the approximation by Wentzel
c71.
3. Detector model The following circumstances were taken into consideration: (1) The incident photon flux on the detector emitted by the target has to transmit Be and SLEW (SLEW: super low-energy window; an ultrathin soft X-ray window composed of alternate layers of polymer and aluminium, providing excellent rejection of UV, IR and visible light and forming an impervious barrier to all gases) windows, a goldcontact, an ice-layer and a Si dead layer before it can be detected in the Si crystal. Then the model assumes for the efficiency E=t
Be t. ,ce tAu tSLEW
t SI.f esc (1 - eeBld),
(4)
where t denotes the transmittance of the successive layers and fesc corrects for escape losses. The last term describes the reduction of E due to the transmittance of the depletion layer. Up to 14 keV the
J. Tschischgale
et al. /Nucl. Instr. and Meth. in Php
389
Res. A 400 (1997) 387-391
I,IIII1IIS
0
2000
4000
6000
8000
1OOCNJ 12000 14000 16000 18000
energy I eV
Fig. 1. Comparison of electron bremsstrahlung spectra from a thick iron target. The inked line characterises the approximation by Wentzel (divided by hv) and the dotted one the Kulenkampff formula.
102 10’ 100
1~~,~l~~~~l~~~~l~~~~I~~~~I~~~~I.~I~I~~~~~~~~~~~~
0
2000
4000
6000
11
8000 10000 12000 14000 16000 18000 energy I eV
Fig. 2. Modelled measurement spectra of electron bremsstrahlung from a thick iron target spectrum considering the actual detector resolution and radiation absorption.
transmittance of the depletion layer of the detector is negligible and reaches 0.3% for 19 keV. (2) Monoenergetic photon radiation produces a Gaussian-shaped full-energy peak accompanied by some tails, escape peaks and a low-energy shelf. By knowing the thickness of the Be-window, the SLEW-window, the gold-contact and of the Si dead
layer, the contribution of radiation absorption can be used to correct the calculated spectrum here the thickness of the Si dead layer was known from the manufacturer’s specification [9]. The spectra model is calculated as a convolution of the corrected spectrum with the actual detector resolution (see Fig. 2).
390
J. Tschischgale et al. lNuc1. Instr. and Meth. in Phys. Res. A 400 (1997) 387-391
In our case, a RijNTEC EDR288 Si(Li) detector [9] with an energy resolution of better than 144 eV at 5.9 keV photon energy was used. The course of the detector efficiency was calculated by reduced x2 fitting the parameters (I, b, c according to the equation
detector
m(E) = a(1 - ebE+c)s(E),
Fig. 3. Experimental a Si(Li) detector.
set-up
for the efficiency
calibration
of
4. Experiment
The experimental set-up is shown in Fig. 3. An X-ray tube with an iron anode was used. The tube voltage was 19 kV, i.e., a bremsstrahlung spectrum with quanta up to 19 keV was measured. This means, that the detector efficiency can be determined up to photon energies of 19 keV. In principle, with this set-up it is also possible to determine the efficiencies for higher quantum energies. Since the flux of incident electrons inside the X-ray tube cannot be measured precisely, only relative detector efficiencies could be determined.
Fig. 4. Result of the detector calibration of a Si(Li) detector window [lo].
(5)
where m(E) stands for the measured spectrum, s(E) for the model spectrum (contribution from the Bewindow, SLEW-window, gold layer, Si-deadlayer) and a, 6, c for fit factors in a often used adaptor function for detector efficiency calibration describing all uncertainties in the chosen model. The error of the fit parameters was determined to about 5% using the covariance matrix. The resulting relative detector efficiency shown in Fig. 4 is a product of all absorption factors and the adaptor function. A comparison with other calibration results for Si(Li) detectors with similar geometries and windows is done in Fig. 4. Efficiencies publicated in commercial catalogues [lo] as well as from calibration on a synchrotron light source [ 1l] agree will with our results derived from the analysis of the electron bremsstrahlung spectra. Especially in the very sensitive low-energy region, the described calibration method delivers efficiency values not sub-
efficiency calibration using electron bremsstrahlung. Solid line - own calibration results; ( +) efficiency [ll] of the same kind as used in this paper, (0) efficiency of a 3 mm thick Si(Li) detector with an 7.5 pm Be
J. Tschischgale
et al. /Nucl. Instr. and Meth. in Phvs. Res. A 400 (1997) 387-391
391
stantially deviating from results of other calibration techniques.
5. Conclusions The presented method allows to determine the relative efficiency of radiation detectors in the lowenergy region in a simple way. The experimental set-up is of the type available in most laboratories. The precision of the derived results could be improved using more recent calculation results for the description of the electron bremsstrahlung production process. Known are cross-sections including contributions from ordinary and atomic bremsstrahlung processes taking into consideration the thresholds of many-electron subshells [12]. Another problem in determining the relative detector efficiency is the use of a thick target for bremsstrahlung production. Here, the use of gases could lead to further improvement of the procedure in the light of the fact that for gases very detailed calculations of bremsstrahlung cross sections are known
c131. Acknowledgements
This work was supported by the BMBF (contract No. 06 DD 111) and the DFG (contract No. Zs 14/4-2).
B. Denecke, G. Grosse, U. Watjen, W. Bambynek, C. Balloux, Nucl. Instr. and Meth. A 286 (1990) 474. Cl1 L.C. Pripedi, P.N. Tandon, Nucl. Instr. and Meth. B 69 (1992) 178. c31 F. Scholze, G. Ulm, Nucl. Instr. and Meth. A 339 (1994) 49. M M. Krumrey, E. Tegeler, Rev. Sci. Instr. 63 (1992) 797. PI C.A. Baker, C.J. Batty, S. Sakamoto, Nucl. Instr. and Meth. A 259 (1987) 501. [61 H.A. Kramers, Philos. Mag. 46 (1923) 836. [71 G. Wentzel, Z. Phys. 27 (1924) 257. PI H. Kulenkampff, Ann. Phys. 69 (1922) 548. c91 Ri)NTEC Info l/93, RdNTEC GmbH, Berlin 1993. Cl01 Canberra product catalogue 81-82, Meriden, 1981, p. 58. Cl11 F. Eggert. M. Krumrey, Rev. Sci. Instr. 62 (1991) 741. L-121A.V. Karol, A.G. Lyalin, A.V. Solovyov, Phys. Rev. A 52 (1995) 1. Cl31 A.V. Korol. A.G. Lyalin, A.V. Solvyov, Bremsstrahlung Spectra of l-1 5 keV electrons on Ar, Abstracts of the 17th Int. Conf. X-Ray and Inner-Shell Processes, Hamburg, 9-13 September 1996, p. 163.
ELSEVIER
Instruments
and Methods
in Physics
Research
SecttonA
A 400 (1997) 387-391
Efficiency calibration of a Si(Li) detector in the low-energy region using electron bremsstrahlung J. Tschischgale, D. Kichler, Technische
U. Lehnert, G. Zschornack”
UniversitZit Dresden, FR Physik, Institut fiir Kern- und Teilchenphysik, Received
10 February
MommsenstraJe
13, D-01062 Dresden, Germanv
1997; received in revised form 18 June 1997
Abstract
In the low-energy region the determination of the detector efficiency is complicated by the fact of nonavailability of certificated calibration sources. To solve this problem the use of electron bremsstrahlung for determining the relative photon detection efficiency of a Si(Li) detector in the low-energy range OS-19 keV is proposed. The calibration is based on energy dispersive measurements of electron bremsstrahlung emitted by an X-ray tube. Model spectra are computed from thick-target bremsstrahlung spectra in a semiclassical approximation and from a physical model for the detector response. Model spectra are fitted to the measured spectra using a parametric adaptor term. Thereby, the error of the determined detector efficiency is approximately 5%.
1. Introduction
Efficiency calibrations of Si(Li) detectors at photon energies below 5 keV are still of great interest for a wide field of applications, but the lack of radionuclide standards in this energy range is a serious problem. For higher energies in the energy range above 5 keV a manifold of calibration sources with well-known photon energies and certificated activities are known. In recent years, the importance of the determination of the spectral quantum detection efficiency E increases because of the development of low-noise analog electronics and new types of entrance windows in the soft X-ray region. Thus, different ap-
*Corresponding
author
0168-9002/97/$17.00 (0 1997 Elsevier Science B.V. All rights reserved PII SO1 68-9002(97)00958-3
proaches have been made to solve the problem by preparing fluorescence sources, which are calibrated by using proportional counters [l] or PIXE cross-sections as in Ref. [2]. Other ways are the use of synchrotron radiation from an electron storage ring as a primary standard source [3,4] and the use of a commercially available fluorescence X-ray source in connection with measurements at several energies, above and below the Si K absorption edge, and at several X-ray beam incidence angles
L-51. An alternative method to solve the above-mentioned problem is the spectrometry of electron bremsstrahlung spectra and the subsequent deconvolution of the detector efficiency using known electron bremsstrahlung cross-sections. Thus, we have calibrated a Si(Li) detector in the energy region from 0.5 keV to 19 keV with the electron
388
J. Tschischgale et al./Nucl. lnstr. and Meth. in Phys. Res. A 400 (1997) 387-391
bremsstrahlung emitted by an X-ray tube. In this way, the course of the detector efficiency was determined independent of calibration sources emitting discrete X-ray or y lines and without using big basic machines like electron storage rings.
deeper the electron moves into the thick target. Thus, the intensity of a thick-target spectrum becomes -z/3 1,
-
~~213
~
! 2. Calculation spectra
of thick-target
(I+
bremsstrahlung
A semiclassical approximation for the description of continuous thick-target electron bremsstrahlung spectra was developed by Kramers [6] and Wentzel [7]. Wentzel calculated the bremsstrahlung spectrum, analysing the classical electron-nucleus interaction and introducing quantum mechanics by the Bohr correspondence principle. Thereby, it is assumed that an incident electron is accelerated by high voltage and the maximum frequency of an emitted photon may only be vo=-,
eU h
(1)
the so-called Duane-Hunt limit. At very low electron energies electronelectron collisions predominate, but the emitted electron bremsstrahlung is of very low energy. At higher energies the bremsstrahlung is caused by the deflection (deceleration) of the incident electron in the Coulomb field of a nucleus. Thereby, the electron will describe a hyperbolic orbit, e.g:this deflection in the Coulomb field of the nucleus will always be an accelerated motion and radiation will be emitted. The intensity radiated by an electron is characterised by the Poynting vector which is determined by the motion of the electron. Thus, the total energy loss can be found by integrating the Poynting vector over time. To obtain the spectral distribution, the electromagnetic radiation is expressed in terms of the dipole momentum of an electron harmonically oscillating about some point. Following Wentzel, the Fourier integral of frequencies for the motion along the hyperbola correspond to the frequencies of emitted radiation. After calculating the mean of all possible hyperbolas, we have to take into account that the electron has lost some energy, so that, as the maximal frequency decreases, the
0.2lS(Zfi(f&
-+=J3)),
(2)
where I, is the intensity radiated in v . v + dv, v. the maximum frequency, v the frequency, Z the atomic number and R the Rydberg constant. In the discussed case, the proportionality shown in Eq. (2) is sufficient to calculate the relative detector efficiency behaviour. For more detailed information on deducing the Wentzel formula see Ref. [7]. For higher energies, this formula is in agreement with Kulenkampff’s [8] empirical equation 1s - Z((v, - v) + aZ).
(3)
A comparison of results from Eq. (2) and the Kuhlenkampff’s formula is given in Fig. 1. As the better based physical description we use in our calculations results of the approximation by Wentzel
c71.
3. Detector model The following circumstances were taken into consideration: (1) The incident photon flux on the detector emitted by the target has to transmit Be and SLEW (SLEW: super low-energy window; an ultrathin soft X-ray window composed of alternate layers of polymer and aluminium, providing excellent rejection of UV, IR and visible light and forming an impervious barrier to all gases) windows, a goldcontact, an ice-layer and a Si dead layer before it can be detected in the Si crystal. Then the model assumes for the efficiency E=t
Be t. ,ce tAu tSLEW
t SI.f esc (1 - eeBld),
(4)
where t denotes the transmittance of the successive layers and fesc corrects for escape losses. The last term describes the reduction of E due to the transmittance of the depletion layer. Up to 14 keV the
J. Tschischgale
et al. /Nucl. Instr. and Meth. in Php
389
Res. A 400 (1997) 387-391
I,IIII1IIS
0
2000
4000
6000
8000
1OOCNJ 12000 14000 16000 18000
energy I eV
Fig. 1. Comparison of electron bremsstrahlung spectra from a thick iron target. The inked line characterises the approximation by Wentzel (divided by hv) and the dotted one the Kulenkampff formula.
102 10’ 100
1~~,~l~~~~l~~~~l~~~~I~~~~I~~~~I.~I~I~~~~~~~~~~~~
0
2000
4000
6000
11
8000 10000 12000 14000 16000 18000 energy I eV
Fig. 2. Modelled measurement spectra of electron bremsstrahlung from a thick iron target spectrum considering the actual detector resolution and radiation absorption.
transmittance of the depletion layer of the detector is negligible and reaches 0.3% for 19 keV. (2) Monoenergetic photon radiation produces a Gaussian-shaped full-energy peak accompanied by some tails, escape peaks and a low-energy shelf. By knowing the thickness of the Be-window, the SLEW-window, the gold-contact and of the Si dead
layer, the contribution of radiation absorption can be used to correct the calculated spectrum here the thickness of the Si dead layer was known from the manufacturer’s specification [9]. The spectra model is calculated as a convolution of the corrected spectrum with the actual detector resolution (see Fig. 2).
390
J. Tschischgale et al. lNuc1. Instr. and Meth. in Phys. Res. A 400 (1997) 387-391
In our case, a RijNTEC EDR288 Si(Li) detector [9] with an energy resolution of better than 144 eV at 5.9 keV photon energy was used. The course of the detector efficiency was calculated by reduced x2 fitting the parameters (I, b, c according to the equation
detector
m(E) = a(1 - ebE+c)s(E),
Fig. 3. Experimental a Si(Li) detector.
set-up
for the efficiency
calibration
of
4. Experiment
The experimental set-up is shown in Fig. 3. An X-ray tube with an iron anode was used. The tube voltage was 19 kV, i.e., a bremsstrahlung spectrum with quanta up to 19 keV was measured. This means, that the detector efficiency can be determined up to photon energies of 19 keV. In principle, with this set-up it is also possible to determine the efficiencies for higher quantum energies. Since the flux of incident electrons inside the X-ray tube cannot be measured precisely, only relative detector efficiencies could be determined.
Fig. 4. Result of the detector calibration of a Si(Li) detector window [lo].
(5)
where m(E) stands for the measured spectrum, s(E) for the model spectrum (contribution from the Bewindow, SLEW-window, gold layer, Si-deadlayer) and a, 6, c for fit factors in a often used adaptor function for detector efficiency calibration describing all uncertainties in the chosen model. The error of the fit parameters was determined to about 5% using the covariance matrix. The resulting relative detector efficiency shown in Fig. 4 is a product of all absorption factors and the adaptor function. A comparison with other calibration results for Si(Li) detectors with similar geometries and windows is done in Fig. 4. Efficiencies publicated in commercial catalogues [lo] as well as from calibration on a synchrotron light source [ 1l] agree will with our results derived from the analysis of the electron bremsstrahlung spectra. Especially in the very sensitive low-energy region, the described calibration method delivers efficiency values not sub-
efficiency calibration using electron bremsstrahlung. Solid line - own calibration results; ( +) efficiency [ll] of the same kind as used in this paper, (0) efficiency of a 3 mm thick Si(Li) detector with an 7.5 pm Be
J. Tschischgale
et al. /Nucl. Instr. and Meth. in Phvs. Res. A 400 (1997) 387-391
391
stantially deviating from results of other calibration techniques.
5. Conclusions The presented method allows to determine the relative efficiency of radiation detectors in the lowenergy region in a simple way. The experimental set-up is of the type available in most laboratories. The precision of the derived results could be improved using more recent calculation results for the description of the electron bremsstrahlung production process. Known are cross-sections including contributions from ordinary and atomic bremsstrahlung processes taking into consideration the thresholds of many-electron subshells [12]. Another problem in determining the relative detector efficiency is the use of a thick target for bremsstrahlung production. Here, the use of gases could lead to further improvement of the procedure in the light of the fact that for gases very detailed calculations of bremsstrahlung cross sections are known
c131. Acknowledgements
This work was supported by the BMBF (contract No. 06 DD 111) and the DFG (contract No. Zs 14/4-2).
B. Denecke, G. Grosse, U. Watjen, W. Bambynek, C. Balloux, Nucl. Instr. and Meth. A 286 (1990) 474. Cl1 L.C. Pripedi, P.N. Tandon, Nucl. Instr. and Meth. B 69 (1992) 178. c31 F. Scholze, G. Ulm, Nucl. Instr. and Meth. A 339 (1994) 49. M M. Krumrey, E. Tegeler, Rev. Sci. Instr. 63 (1992) 797. PI C.A. Baker, C.J. Batty, S. Sakamoto, Nucl. Instr. and Meth. A 259 (1987) 501. [61 H.A. Kramers, Philos. Mag. 46 (1923) 836. [71 G. Wentzel, Z. Phys. 27 (1924) 257. PI H. Kulenkampff, Ann. Phys. 69 (1922) 548. c91 Ri)NTEC Info l/93, RdNTEC GmbH, Berlin 1993. Cl01 Canberra product catalogue 81-82, Meriden, 1981, p. 58. Cl11 F. Eggert. M. Krumrey, Rev. Sci. Instr. 62 (1991) 741. L-121A.V. Karol, A.G. Lyalin, A.V. Solovyov, Phys. Rev. A 52 (1995) 1. Cl31 A.V. Korol. A.G. Lyalin, A.V. Solvyov, Bremsstrahlung Spectra of l-1 5 keV electrons on Ar, Abstracts of the 17th Int. Conf. X-Ray and Inner-Shell Processes, Hamburg, 9-13 September 1996, p. 163.