Photon interaction with semiconductor and scintillation detectors

Photon interaction with semiconductor and scintillation detectors 1 corresp first-author Corresponding author Email: kudphyvps@rediffmail.com Corresponding author Email: kudphyvps@rediffmail.com kudphyvps@rediffmail.com 1 Department of Physics, Karnatak University, Dharwad 580003, India Department of Physics, Karnatak University, Dharwad 580003, India Mass attenuation coefficients, effective atomic numbers, and electron densities for semiconductor and scintillation detectors have been calculated in the photon energy range 1 keV–100 GeV. These interaction parameters have been found to vary with detector composition and the photon energy. The variation of the parameters with energy is shown graphically for all the partial photon interaction processes. The effective atomic numbers of the detector were compared with the ZXCOM program, and the results were found to be comparable. Efficiencies of semiconductor and scintillation detectors are presented in terms of effective atomic numbers. The study should be useful for comparing the detector performance in terms of gamma spectroscopy, radiation sensitivity, radiation measurement, and radiation damage. The results of the present investigation should stimulate research work for gamma spectroscopy and radiation measuring materials. semiconductor scintillation attenuation coefficients Z eff 1 Introduction 1 Radiation interaction with elements, compounds, and composite materials has become a thrust area of research and development to investigate material properties and their various applications. The process of radiation interaction is being used for various applications in nuclear physics, radiation physics, radiation detection, radiobiology, medicine, agriculture, and industry. The mass attenuation coefficients, effective atomic numbers, and effective electron densities are basic quantities required to study the photon interactions. The interaction depends on incident photon energy and elements of the absorbing material (i.e. atomic number). In a compound or composite material(e.g. concrete, polymer, alloy, biological material, etc.)the atomic number is represented by an effective atomic number analogous to the atomic number of a single element. The effective atomic number varies with photon energy, whereas the atomic number of element is constant for all photon energies. Semiconductors and scintillation detectors are widely used for X- and gamma-ray measurements. These detectors are utilized in different fields of science and technology, mainly for identification of gamma-ray emitters and sometimes only for radiation detection. The sensitivity for gamma-ray detection is essential for the identification of radiation and different isotopes. Scintillation detectors have a much greater efficiency for interactions with gamma-rays compared to gas and liquid filled detectors. Semiconductor-based detectors have shown better energy resolution and good stability over time, temperature, and operating parameters. The instruments consist of scintillation and semiconductor detectors to provide the measure of the energy of a radiation interaction and the type of radionuclide. The scintillation and semiconductor-based detectors are being used in nuclear physics laboratories, research reactors, nuclear power plants, and accelerators. These detectors are being utilized in laboratories and industries for gamma-ray detection in on-line and off-line measurements based on the requirements and characteristic suitability. The mechanisms for measurement of the energy of the photon and the type of radionuclide require detailed information about the interaction with an element or a compound. The interaction probability (scattered/absorbed) per unit length of a photon with an atom is described by the mass attenuation coefficient (fundamental interaction parameter). The mass attenuation coefficient is utilized for the calculation of the effective atomic number and the effective electron density of a compound or composite material. Therefore, knowledge of the mass attenuation coefficient, effective atomic number, and effective electron density are essential in comparing the detector efficiency and resolution. Studies on effective atomic numbers and electron densities have been reported by several investigators for chemical compounds [ 1 1 - 2 2 1-2 ],low- Z materials [ 3 3 - 4 4 3-4 ], alloys and steels [ 5 5 - 8 8 5-8 ], glass and minerals [ 9 9 - 12 12 9-12 ], biological materials [ 13 13 ], detectors[ 14 14 - 15 15 14-15 ],tissue substitutes[ 16 16 - 18 18 16-18 ], and composites [ 19 19 ]. There are some studies which calculate the effective atomic numbers of semiconductors [ 20 20 - 22 22 20-22 ]in the literature. The radiation damage of some widely used semiconductor materials has been simulated using FLUKA[ 23 23 ].This has encouraged us to calculate the effective atomic numbers and electron densities, which should be directly applicable to gamma spectroscopy, radiation sensitivity, radiation measurement, and radiation damage. 2 Computational method and theoretical background 1 The mass attenuation coefficients of a compound or composite material are determined by the transmission method using Lambert-Beer’s law (), where I 0 and I are the incident and attenuated photon intensity with energy E , respectively, µ m =  μ / ρ  (cm 2 .g -1 ) is the mass attenuation coefficient, and t (g/cm 2 ) is the mass thickness of the medium (the mass per unit area).The total  μ m  value for materials composed of multi elements is the sum of the ( μ m ) i  values of each constituent element obtained by the following mixture rule, ( <math id="M1"><mrow><msub><mi>μ</mi><mi>m</mi></msub><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mi>i</mi><mi>n</mi></munderover><mrow><msub><mi>w</mi><mi>i</mi></msub></mrow></mstyle><msub><mrow><mo stretchy="false">(</mo><mi>μ</mi><mo>/</mo><mi>ρ</mi><mo stretchy="false">)</mo></mrow><mi>i</mi></msub></mrow></math> ), where <math id="M2"><mrow><msub><mi>w</mi><mi>i</mi></msub></mrow></math> is the proportion by weight and <math id="M3"><mrow><msub><mrow><mo stretchy="false">(</mo><mi>μ</mi><mo>/</mo><mi>ρ</mi><mo stretchy="false">)</mo></mrow><mi>i</mi></msub></mrow></math> is mass attenuation coefficient of the i th element using the WinXcom program [ 24 24 ],which was updated for XCOM programs [ 25 25 ]. The quantity w i is given by <math id="M4"><mrow><msub><mi>w</mi><mi>i</mi></msub><mo>=</mo><msub><mi>n</mi><mi>i</mi></msub><msub><mi>A</mi><mi>i</mi></msub><mo>/</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mi>j</mi><mi>n</mi></munderover><mrow><msub><mi>n</mi><mi>j</mi></msub></mrow></mstyle><msub><mi>A</mi><mi>j</mi></msub></mrow></math> with the condition <math id="M5"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mi>i</mi><mi>n</mi></munderover><mrow><msub><mi>w</mi><mi>i</mi></msub></mrow></mstyle><mo>=</mo><mn>1</mn></mrow></math> , where A i is the atomic weight of the i th element and n i is the number of formula units. The total atomic cross-sections ( σ t ) for a compound or composite material can be obtained from the measured  μ m  values using the following relation [ 26 26 ]; <math display="block" id="M6"><mrow><msub><mi>σ</mi><mi>t</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mi>m</mi></msub><mi>M</mi></mrow><mrow><msub><mi>N</mi><mi>A</mi></msub><mo>,</mo></mrow></mfrac></mrow></math> where  <math id="M7"><mrow><mi>M</mi><mo>=</mo><mstyle displaystyle="true"><munderover><mo>∑</mo><mi>i</mi><mi>n</mi></munderover><mrow><msub><mi>n</mi><mi>i</mi></msub></mrow></mstyle><msub><mi>A</mi><mi>i</mi></msub></mrow></math> is the molecular weight of a compound or composite material and  N A  is Avogadro's number. The effective atomic cross section ( σ a ) can be calculated by the following equation: <math display="block" id="M8"><mrow><msub><mi>σ</mi><mi>a</mi></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mi>A</mi></msub></mrow></mfrac><mstyle displaystyle="true"><mo>∑</mo><mrow><msub><mi>f</mi><mi>i</mi></msub><msub><mi>A</mi><mi>i</mi></msub></mrow></mstyle><msub><mrow><mo stretchy="false">(</mo><mfrac><mi>μ</mi><mi>ρ</mi></mfrac><mo stretchy="false">)</mo></mrow><mi>i</mi></msub><mo>.</mo></mrow></math> Total electronic cross-section ( σ e ) for a compound or composite material is calculated using the following equation [ 12 12 ]; <math display="block" id="M9"><mrow><msub><mi>σ</mi><mi>e</mi></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mi>A</mi></msub></mrow></mfrac><mstyle displaystyle="true"><mo>∑</mo><mrow><mfrac><mrow><msub><mi>f</mi><mi>i</mi></msub><msub><mi>A</mi><mi>i</mi></msub><msub><mrow/><mrow/></msub></mrow><mrow><msub><mi>Z</mi><mi>i</mi></msub></mrow></mfrac></mrow></mstyle><msub><mrow><mo stretchy="false">(</mo><mfrac><mi>μ</mi><mi>ρ</mi></mfrac><mo stretchy="false">)</mo></mrow><mi>i</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>σ</mi><mi>a</mi></msub></mrow><mrow><msub><mi>Z</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></mrow></mfrac><mo>,</mo></mrow></math> where  <math id="M10"><mrow><msub><mi>f</mi><mi>i</mi></msub><mo>=</mo><mfrac><mrow><msub><mi>n</mi><mi>i</mi></msub></mrow><mrow><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder><mrow><msub><mi>n</mi><mi>i</mi></msub></mrow></mstyle></mrow></mfrac></mrow></math> denotes the fractional abundance of the element  i  with respect to the number of atoms, such that <math id="M11"><mrow><mstyle displaystyle="true"><munderover><mo>∑</mo><mi>i</mi><mi>n</mi></munderover><mrow><msub><mi>f</mi><mi>i</mi></msub></mrow></mstyle><mo>=</mo><mn>1</mn></mrow></math> ,  Z i  is the atomic number of the i th element. σ a  and  σ e  are related to the effective atomic number ( Z eff ) of a compound or composite material through the following relation [ 12 12 ]; <math display="block" id="M12"><mrow><msub><mi>Z</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>σ</mi><mi>a</mi></msub></mrow><mrow><msub><mi>σ</mi><mi>e</mi></msub></mrow></mfrac><mo>.</mo></mrow></math> The effective electron density, N el (number of electrons per unit mass) of a compound or composite material is derived from following relation: <math display="block" id="M13"><mrow><msub><mi>N</mi><mrow><mi>e</mi><mi>l</mi></mrow></msub><mo>=</mo><mfrac><mrow><mo stretchy="false">(</mo><mfrac><mi>μ</mi><mi>ρ</mi></mfrac><mo stretchy="false">)</mo></mrow><mrow><msub><mi>σ</mi><mi>e</mi></msub></mrow></mfrac><mo>=</mo><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>Z</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></mrow><mi>M</mi></mfrac></mrow><mo>)</mo></mrow><msub><mi>N</mi><mi>A</mi></msub><munder><mo>∑</mo><mi>i</mi></munder><msub><mi>n</mi><mi>i</mi></msub><mo>.</mo></mrow></math> Recently, a program, direct- Z eff , has been developed for the calculation of mass attenuation coefficients, effective atomic numbers, and effective electron densities for a compound or composite material for photon energies of 1 keV to 100 GeV[ 27 27 ].In the present investigation, the direct- Z eff program was used to calculate mass attenuation coefficients, effective atomic numbers, and effective electron densities of semiconductor and scintillation detectors. 3 Results and discussion 1 The most popular semiconductor and scintillation detectors were chosen in the present investigation. By using their chemical compositions, the mass attenuation coefficients ( μ /ρ), effective atomic numbers ( Z eff ) and effective electron densities ( N el )were calculated in the photon energy range of 1 keV to 100 GeV. In the following subsections, energy and chemical composition dependencies of the μ/ρ, Z eff , and N el for total and partial interaction is discussed. 3.1 Total (with coherent) photon interaction 2 The total mass attenuation coefficients, μ /ρ, of the semiconductor and scintillation detectors in the photon energy range of 1 keV to 100 GeV is shown in Fig.1 Fig.1 . The variations in theμ/ρare due to the chemical composition and energy dependency. In the low energy region, μ/ρhave the highest values, where the photoelectric effect is dominant and the interaction cross-section is proportional to Z 4–5 /E 3.5 . In the intermediate energy region, the incoherent scattering is the dominant interaction process. There is a linear Z-dependence of incoherent scattering and the μ /ρ is found to be constant. In the high energy region, μ /ρincrease, where the pair production is dominant and the interaction cross section is proportional to Z 2 . For the total photon interaction process, the variations of Z eff and N el with photon energies are shown in Figs.2 Figs.2 and 3 3 , respectively. From Fig. 2 Fig. 2 , it is clear Z eff increases with energy initially and then decreases up to 2 MeV (approx.) . Above 100 MeV, Z eff remains almost constant for all the detectors. This is due to the dominance of pair production in the high energy region. In Fig.3 Fig.3 , the variations of N el with photon energy for the total interaction processes are similar to that of Z eff and can be explained similarly. From Fig. 2 Fig. 2 , it is observed that the variation of Z eff depends upon the chemical compositions of the detectors. The PbI 2 detectors containa larger Z (Pb) value than any of the other detectors due to the largest Z eff to be observed. The LSO and LuAP detectors show a sharp jump in Z eff with energy due to the composition of the low-andhigh-Z elements. The variation of Z eff for total interaction reflects the importance of the partial photon interaction processes. The dominating photon interaction process is the photoelectric absorption atlow energies, incoherent (Compton) scattering at intermediate energies, and pair production at high energies. Coherent (Rayleigh) scattering doesn’t plays any significant role, since it occurs mainly at low energies, where the photoelectric effect is the most important interaction process. At a low-energy range ( E < 0.01 MeV), the maximum Z eff is found where the Z 4-5 dependence of theinteraction cross section for the photoelectric effect contributesto the highest-Z of the detector.At the intermediate energy range (0.05 MeV < E < 5 MeV), Compton scattering is the main photon interaction process. At high energies (typically E > 100 MeV), Z eff becomes constant again, but smaller than in the low-energy range. This is due to the dominance of pair production. Hence, pair production provides less of a contribution to the higher-Z elements than the photoelectric effect. It is to be noted that the effective atomic numbers of the detectors are found to be constant in the pair production region ( E > 100 MeV). The largest Z eff value among the selected semiconductor and scintillation detectors was observed for PbI 2 , followed by HgI 2 . The values of Z eff show that the interaction probability of the photon with the detectors is the largest,whereas it is the lowest for YAG.The largest interaction probability of the photon with the PbI 2 provides the highest efficiency of the detector. Therefore, the efficiency of semiconductor and scintillation detectors are presented in terms of effective atomic numbers.However, the PbI 2 is not a suitable detector because the electron-hole pair creation requires an energy value of 7.68 eV, which is very large compared to 2.96 eV for the Ge detector [ 28 28 ].During the selection of a suitable detector, photon interaction characteristics should be compared for each parameter in order to get the desired results. 3.2 Photoelectric absorption 2 For the photoelectric absorption process, the variations in Z eff and N el with photon energy are shown in Figs. 4 Figs. 4 and 5 5 , respectively. Fig.4 Fig.4 shows the most significant variations in Z eff aredue to the chemical compositions of the detectors. Below 10 keV, the variations in Z eff are more pronouncedin the detectors containing high-Z elements, and there isno variation in the CdTe, GaAs, and GaSe detectors, except for a few energies.The sensitivity of these detectors is low;however, the behaviors of Z eff for all detectors are similar after 100 MeV. The variation of N el for photoelectric absorption shown in Fig.5 Fig.5 can be explained similarlyto Fig. 4 Fig. 4 . 3.3 Incoherent (Compton) scattering 2 For incoherent scattering, the variations in Z eff and N el with photon energy are shown in Figs. 6 Figs. 6 and 7 7 , respectively. From Fig. 6 Fig. 6 , it is found that Z eff increases sharply with an increase inthe energy region 1–500 keV. Beyond 1 MeV, Z eff is independent of photonenergy for all the detectors. The variation of Z eff depends on the respective proportion of the atomic number of the elements inthe detectors.The variation of N e l for Compton (coherent)scattering in Fig.7 Fig.7 can be explained using the partial photon interaction process. 3.4 Coherent (Rayleigh) scattering 2 For the coherent scattering, the variations in Z eff and N el with photon energy are shown in Figs. 8 Figs. 8 and 9 9 , respectively. From Fig.8 Fig.8 , it is found that Z eff is constant except for the detectors that increase in energy from 1 keV to 1 MeV. Beyond 1 MeV, Z eff is independent of photon energy for all the detectors. The variation of N el for Compton (coherent) scattering in Fig.9 Fig.9 can be explained similarly to Fig.8 Fig.8 . Fig. 10 Fig. 10 shows the variation of the coherent to incoherent scattering ratio ( Coh./Incoh. ) for the Z eff of all the detectors,and is constant for photon energies beyond 1 MeV. 3.5 Pair production (nuclear field) 2 For pair production in the nuclear field, the variations of Z eff and N el with photon energy are shown in Figs. 11 Figs. 11 and 12 12 , respectively. From Fig. 11 Fig. 11 , it is found that Z eff slightly decreases (for few detectors) with an increase in photon energy ranging from1 to 20 MeV, and then it is almost independent of photon energy for all other detectors. The variation of N el for pair production (nuclear) in Fig. 12 Fig. 12 can be explained similarly to Fig. 11 Fig. 11 . 3.6 Pair production (electric field) 2 For the pair production in the electric field, the variations of Z eff and N el with photon energy are shown in Figs. 13 Figs. 13 and 14 14 , respectively. From Fig. 13 Fig. 13 , it is found that Z eff is independent of photon energy, except for the YAG, AlSb, LSO, and LuAP detectors. Also, Z eff for the YAG, AlSb, LSO, and LuAP detectors becomes independent of photon energy beyond 1000 MeV. The highest-Z containing detector (PbI 2 ) is found to have the highest Z eff .The variation of N el for pair production (electric) in Fig. 14 Fig. 14 can be explained similarly to Fig.13 Fig.13 . In Fig. 15 Fig. 15 , the ratio of effective atomic numbers for pair production for nuclear to electric is shown and found to be independent from energy, except for LuAP and LSO. 3.7 Comparison with ZXCOM 2 The effective atomic numbers calculated using Eq.(4) were compared with ZXCOM software [ 29 29 ]. In the ZXCOM process, the effective atomic number is characterized using Rayleigh and Compton scattering. İçelli [ 30 30 ] showed the theoretical and computational approach for obtaining data from the R/C ratio (R). Details of the ZXCOM method and theoretical approach for calculation are reported in the literature [ 29 29 - 30 30 29-30 ]. The effective atomic numbers using both methods are given in Table 1 Table 1 . From Table 1 Table 1 , it is found that effective atomic numbers calculated using direct- Z eff and ZXCOM are comparable with each other, with theexception of a few energies. Energy (MeV)   Method CdTe CdZnTe HgI2 GaAs PbI 2 GaSe AlSb YAG LSO LuAP 1 2 10 -2 1 1 Direct-Z eff 1 1 50.24 1 1 41.43 1 1 60.60 1 1 32.10 1 1 61.64 1 1 32.71 1 1 45.87 1 1 26.00 1 1 64.73 1 1 62.49 1 1 ZXCOM 1 1 50.19 1 1 46.29 1 1 66.51 1 1 32.02 1 1 67.32 1 1 32.53 1 1 45.80 1 1 28.64 1 1 64.62 1 1 62.23 1 2 10 -1 1 1 Direct-Z eff 1 1 50.22 1 1 47.80 1 1 68.87 1 1 32.07 1 1 70.44 1 1 32.67 1 1 48.06 1 1 25.19 1 1 65.55 1 1 63.95 1 1 ZXCOM 1 1 50.25 1 1 47.91 1 1 63.92 1 1 32.01 1 1 64.71 1 1 32.58 1 1 47.44 1 1 21.95 1 1 62.67 1 1 60.56 1 2 10 0 1 1 Direct-Z eff 1 1 50.02 1 1 43.62 1 1 63.40 1 1 32.00 1 1 64.33 1 1 32.50 1 1 32.77 1 1 14.04 1 1 27.27 1 1 23.98 1 1 ZXCOM 1 1 50.36 1 1 48.77 1 1 71.92 1 1 32.12 1 1 73.76 1 1 32.79 1 1 49.61 1 1 34.99 1 1 68.37 1 1 67.54 1 2 10 1 1 1 Direct-Z eff 1 1 50.05 1 1 44.58 1 1 63.60 1 1 32.02 1 1 64.48 1 1 32.54 1 1 38.09 1 1 16.79 1 1 38.26 1 1 33.92 1 1 ZXCOM 1 1 50.41 1 1 49.04 1 1 73.59 1 1 32.13 1 1 75.57 1 1 32.82 1 1 49.81 1 1 35.34 1 1 68.95 1 1 68.29 1 2 10 2 1 1 Direct-Z eff 1 1 50.07 1 1 45.13 1 1 63.98 1 1 32.03 1 1 64.92 1 1 32.56 1 1 41.79 1 1 20.45 1 1 49.07 1 1 44.63 1 1 ZXCOM 1 1 50.50 1 1 49.44 1 1 75.72 1 1 32.15 1 1 77.80 1 1 32.87 1 1 50.09 1 1 36.03 1 1 69.59 1 1 69.15 1 2 10 3 1 1 Direct-Z eff 1 1 50.07 1 1 45.15 1 1 63.94 1 1 32.03 1 1 64.92 1 1 32.56 1 1 41.96 1 1 20.64 1 1 49.52 1 1 45.11 1 1 ZXCOM 1 1 50.50 1 1 49.44 1 1 75.72 1 1 32.15 1 1 77.80 1 1 32.87 1 1 50.09 1 1 36.03 1 1 69.59 1 1 69.15 1 2 10 4 1 1 Direct-Z eff 1 1 50.07 1 1 45.14 1 1 63.96 1 1 32.03 1 1 64.89 1 1 32.56 1 1 41.92 1 1 20.63 1 1 49.45 1 1 45.03 1 1 ZXCOM 1 1 50.50 1 1 49.44 1 1 75.72 1 1 32.15 1 1 77.80 1 1 32.87 1 1 50.09 1 1 36.03 1 1 69.59 1 1 69.15 1 2 10 5 1 1 Direct-Z eff 1 1 50.07 1 1 45.14 1 1 63.93 1 1 32.03 1 1 64.91 1 1 32.56 1 1 41.93 1 1 20.62 1 1 49.45 1 1 45.04 1 1 ZXCOM 1 1 50.66 1 1 49.90 1 1 77.52 1 1 32.18 1 1 79.61 1 1 32.95 1 1 50.32 1 1 36.58 1 1 70.14 1 1 69.86 4 Conclusion 1 In the presentinvestigation, we have calculated mass attenuation coefficients, effective atomic numbers, and effective electron densities for semiconductor and scintillation detectors.The investigation is summarized below; • Effective atomic numbers for semiconductor and scintillation detectors are found to be constant in the pair production region (E> 100 MeV). • Effective atomic numbers calculatedusing thedirect-Z eff and ZXCOM programs are found to be comparable. • Efficiencies of semiconductor and scintillation detectors are presented in terms of effective atomic numbers. 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Practical method for experimental effective atomic number in the coherent to Compton scattering ratio , Journal of Quantitative Spectroscopy and Radiative Transfer , 2006 , 101 : 151 - 158 . doi: 10.1016/j.jqsrt.2005.11.014 http://doi.org/10.1016/j.jqsrt.2005.11.014 . Practical method for experimental effective atomic number in the coherent to Compton scattering ratio The authors are thankful for Yaşar Karabul, the Department of Physics, and Yildiz Technical University of Turkey for providing the results of effective atomic numbers using ZXCOM. 10.1007/s41365-016-0076-8 2015-05-13 2015-10-21 2015-10-22 2016-05-14 2016-06-20 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2016 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-016-0076-8 http://dx.doi.org/10.1007/s41365-016-0076-8 . 2016 Nuclear Science and Techniques 03 27