Photon interaction with semiconductor and scintillation detectors

NUCLEAR PHYSICS AND INTERDISCIPLINARY RESEARCH

Photon interaction with semiconductor and scintillation detectors

V. P. Singh，

N. M. Badiger

Nuclear Science and Techniques

Vol.27, No.3

Article number 72

Published in print 20 Jun 2016

Available online 14 May 2016

DOI：10.1007/s41365-016-0076-8

54500

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.

semiconductorscintillationattenuation coefficientsZeff

1 Introduction

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 [1-2],low-Z materials [3-4], alloys and steels [5-8], glass and minerals [9-12], biological materials [13], detectors[14-15],tissue substitutes[16-18], and composites [19].

There are some studies which calculate the effective atomic numbers of semiconductors [20-22]in the literature. The radiation damage of some widely used semiconductor materials has been simulated using FLUKA[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

The mass attenuation coefficients of a compound or composite material are determined by the transmission method using Lambert-Beer’s law (), where I₀ and I are the incident and attenuated photon intensity with energy E, respectively, µ_m= μ/ρ (cm².g^-1) is the mass attenuation coefficient, and t(g/cm²) 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, ( $μ_{m} = \sum_{i}^{n} w_{i} {(μ / ρ)}_{i}$ ), where $w_{i}$ is the proportion by weight and ${(μ / ρ)}_{i}$ is mass attenuation coefficient of the i^th element using the WinXcom program [24],which was updated for XCOM programs [25]. The quantity w_i is given by $w_{i} = n_{i} A_{i} / \sum_{j}^{n} n_{j} A_{j}$ with the condition $\sum_{i}^{n} w_{i} = 1$ , 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];

σ_{t} = \frac{μ_{m} M}{N_{A},}

(1)

where $M = \sum_{i}^{n} n_{i} A_{i}$ 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:

σ_{a} = \frac{1}{N_{A}} \sum f_{i} A_{i} {(\frac{μ}{ρ})}_{i} .

(2)

Total electronic cross-section (σ_e) for a compound or composite material is calculated using the following equation [12];

σ_{e} = \frac{1}{N_{A}} \sum \frac{f_{i} A_{i}_{}}{Z_{i}} {(\frac{μ}{ρ})}_{i} = \frac{σ_{a}}{Z_{e f f}},

(3)

where $f_{i} = \frac{n_{i}}{\sum_{i} n_{i}}$ denotes the fractional abundance of the element i with respect to the number of atoms, such that $\sum_{i}^{n} f_{i} = 1$ , Z_i is the atomic number of the i^th element. σ_aand σ_eare related to the effective atomic number (Z_eff) of a compound or composite material through the following relation [12];

Z_{e f f} = \frac{σ_{a}}{σ_{e}} .

(4)

The effective electron density, N_el (number of electrons per unit mass) of a compound or composite material is derived from following relation:

N_{e l} = \frac{(\frac{μ}{ρ})}{σ_{e}} = (\frac{Z_{e f f}}{M}) N_{A} \sum_{i} n_{i} .

(5)

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].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

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

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. 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 Z².

Fig.1.

Mass attenuation coefficients of Semiconductor and Scintillation detectors

For the total photon interaction process, the variations of Z_eff and N_el with photon energies are shown in Figs.2 and 3, respectively. From 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, 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.

Fig.2.

Effective atomic numbers (total) of Semiconductor and Scintillation detectors

Fig.3.

Effective electron densities (total) of Semiconductor and Scintillation detectors

From Fig. 2, it is observed that the variation of Z_eff depends upon the chemical compositions of the detectors. The PbI₂detectors 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_effbecomes 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 PbI₂, followed by HgI₂. 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 PbI₂ 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 PbI₂ 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].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

For the photoelectric absorption process, the variations in Z_eff and N_el with photon energy are shown in Figs. 4 and 5, respectively. 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 can be explained similarlyto Fig. 4.

Fig.4.

Effective atomic numbers (photoelectric) of Semiconductor and Scintillation detectors

Fig.5.

Effective electron densities (photoelectric) of Semiconductor and Scintillation detectors

3.3 Incoherent (Compton) scattering

For incoherent scattering, the variations in Z_eff and N_el with photon energy are shown in Figs. 6 and 7, respectively. From 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_el for Compton (coherent)scattering in Fig.7 can be explained using the partial photon interaction process.

Fig.6.

Effective atomic numbers (Incoherent) of Semiconductor and Scintillation detectors

Fig.7.

Effective electron densities (Incoherent) of Semiconductor and Scintillation detectors

3.4 Coherent (Rayleigh) scattering

For the coherent scattering, the variations in Z_eff and N_el with photon energy are shown in Figs. 8 and 9, respectively. From 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 can be explained similarly to Fig.8.

Fig.8.

Effective atomic numbers (coherent) of Semiconductor and Scintillation detectors

Fig.9.

Effective electron densities (coherent) of Semiconductor and Scintillation detectors

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.

Fig.10.

Effective atomic numbers (coherent/Incoherent) of Semiconductor and Scintillation detectors

3.5 Pair production (nuclear field)

For pair production in the nuclear field, the variations of Z_eff and N_el with photon energy are shown in Figs. 11 and 12, respectively. From 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 can be explained similarly to Fig. 11.

Fig.11.

Effective atomic numbers (nuclear pair) of Semiconductor and Scintillation detectors

Fig.12.

Effective electron densities (nuclear pair) of Semiconductor and Scintillation detectors

3.6 Pair production (electric field)

For the pair production in the electric field, the variations of Z_eff and N_el with photon energy are shown in Figs. 13 and 14, respectively. From 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 (PbI₂) is found to have the highest Z_eff.The variation of N_el for pair production (electric) in Fig. 14 can be explained similarly to Fig.13.

Fig.13.

Effective atomic numbers (electrical pair) of Semiconductor and Scintillation detectors

Fig.14.

Effective electron densities (electrical pair) of Semiconductor and Scintillation detectors

In 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.

Fig.15.

Effective atomic numbers (nuclear/electrical) of Semiconductor and Scintillation detectors

3.7 Comparison with ZXCOM

The effective atomic numbers calculated using Eq.(4) were compared with ZXCOM software [29]. In the ZXCOM process, the effective atomic number is characterized using Rayleigh and Compton scattering. İçelli [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 [29-30]. The effective atomic numbers using both methods are given in Table 1. From 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.

Comparison of effective atomic numbers by Direct-Z_eff and ZXCOM

Energy (MeV)	Method	CdTe	CdZnTe	HgI2	GaAs	PbI₂	GaSe	AlSb	YAG	LSO	LuAP
10^-2	Direct-Z_eff	50.24	41.43	60.60	32.10	61.64	32.71	45.87	26.00	64.73	62.49
10^-2	ZXCOM	50.19	46.29	66.51	32.02	67.32	32.53	45.80	28.64	64.62	62.23
10^-1	Direct-Z_eff	50.22	47.80	68.87	32.07	70.44	32.67	48.06	25.19	65.55	63.95
10^-1	ZXCOM	50.25	47.91	63.92	32.01	64.71	32.58	47.44	21.95	62.67	60.56
10⁰	Direct-Z_eff	50.02	43.62	63.40	32.00	64.33	32.50	32.77	14.04	27.27	23.98
10⁰	ZXCOM	50.36	48.77	71.92	32.12	73.76	32.79	49.61	34.99	68.37	67.54
10¹	Direct-Z_eff	50.05	44.58	63.60	32.02	64.48	32.54	38.09	16.79	38.26	33.92
10¹	ZXCOM	50.41	49.04	73.59	32.13	75.57	32.82	49.81	35.34	68.95	68.29
10²	Direct-Z_eff	50.07	45.13	63.98	32.03	64.92	32.56	41.79	20.45	49.07	44.63
10²	ZXCOM	50.50	49.44	75.72	32.15	77.80	32.87	50.09	36.03	69.59	69.15
10³	Direct-Z_eff	50.07	45.15	63.94	32.03	64.92	32.56	41.96	20.64	49.52	45.11
10³	ZXCOM	50.50	49.44	75.72	32.15	77.80	32.87	50.09	36.03	69.59	69.15
10⁴	Direct-Z_eff	50.07	45.14	63.96	32.03	64.89	32.56	41.92	20.63	49.45	45.03
10⁴	ZXCOM	50.50	49.44	75.72	32.15	77.80	32.87	50.09	36.03	69.59	69.15
10⁵	Direct-Z_eff	50.07	45.14	63.93	32.03	64.91	32.56	41.93	20.62	49.45	45.04
10⁵	ZXCOM	50.66	49.90	77.52	32.18	79.61	32.95	50.32	36.58	70.14	69.86

4 Conclusion

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_effand 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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