J. Nig. Soc. Phys. Sci. 4 (2022) 926 Journal of the Nigerian Society of Physical Sciences A comparison of the performance and energy resolution of CdTe and Si detectors in the X-ray Fluorescence studies of metal samples and Alloys Iniobong P. Etima,b,∗, Rebecca Emmanuel Mfonc aDepartment of Physics, University of Surrey Guildford Surrey GU2 7XH, United Kingdom bDepartment of Physics, University of Calabar, P.M.B 1115 Calabar, Cross River State, Nigeria cDepartment of Physics Federal University of Lafia, P.M.B 146 Lafia, Nasarawa State, Nigeria Abstract X-ray fluorescence provides a powerful means of non-destructively determining the elemental composition of a sample. X-rays from a Molybde- num (Mo) source was fired on copper, molybdenum, lead, steel and brass samples to determine their composition and relative abundance of their constituent elements. Two different detectors : the Cadmium Telluride (CdTe) and Silicon(Si) detectors were used to pick up the signals from the scattering of the X-rays at the sample surfaces and their energy resolutions as well as efficiencies were compared. With a non-noisy amplifier, the Si detector had a higher resolution (0.27 % ) when compared to the 0.38 % for the CdTe detector but it had a lower efficiency when compared to that of the CdTe detector. It was also discovered that higher energies produced lower detector efficiencies. DOI:10.46481/jnsps.2022.926 Keywords: X-ray fluorescence, Cadmium Telluride detector, Silicon detector, Energy resolution, energy efficiency Article History: Received: 09 July 2022 Received in revised form: 10 October 2022 Accepted for publication: 11 November 2022 Published: 27 November 2022 c© 2022 The Author(s). Published by the Nigerian Society of Physical Sciences under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Communicated by: Edward Anand Emile 1. Introduction X-ray fluorescence (XRF) is a technique which non-destructively analyses a material to identify the elements that make it up [1]. A material bombarded with high-energy X-rays absorbs it and emits characteristic secondary X-rays of lower energy but higher energy X-rays can also be produced using an X-ray tube [2]. Usually a heated cathode emits electrons, which are accelerated using an electric field to hit a metal target called an anode. When these electrons interact either with the orbit ∗Corresponding author tel. no: +234(0)8034451806 Email address: ini2etim@unical.edu.ng (Iniobong P. Etim ) electrons of the atoms, they produce characteristic X-rays but when they interact with the nuclei of the target, they generate a continuum spectrum (bremsstrahlung radiation) [3]. The continuum spectrum can have energies between zero and the maximum energy of the incident electrons. The X-rays produced are then incident on a sample and if the incident pho- tons have enough energy, they excite or ionize electrons of the inner orbits (photoelectric effect), producing a hole in the inner orbit and making the atom unstable. An electron from the outer orbits moves in to fill that hole resulting in the emission of a photon with energy equal to the energy difference of the initial and final states producing X-ray fluorescence (XRF) [4]. The energy of XRF is measured using a semiconductor de- 1 Etim & Mfon / J. Nig. Soc. Phys. Sci. 4 (2022) 926 2 tector. The signal from the detector is transferred to an ampli- fier and then to a multi-channel analyzer (MCA). The spectrum produced is visible and can be displayed on a computer screen. XRF is used for monitoring compliance with limits set by mon- itoring bodies [5] and for investigating soil samples to ascertain the extent of chemical weathering and possible vulnerability to gully erosion [6]. XRF is also used for forensic geoscience in- vestigations and is a tool for environmental and criminal inves- tigations [7]. XRF can be used to analyze elements in a material as the produced X-rays characterize each element and directly relates its amount in the material. That method is mainly used for metals, ceramics and glasses and apart from that, it is used in Archaeology and Geochemistry. In this experiment, XRF produced from different metals and alloy samples are measured using two types of detectors. The characteristic X-ray peaks emanating from the samples aid the identification of the metals it contains and for alloys, the ratio of the different elements it contains was calculated. The energies of the characteristic X-rays from these samples were also calcu- lated and obtained results were used to identify the metal/metals present in the investigated samples. The resolution and efficien- cies of the two detectors as the angle the sample makes with the X-ray beam direction was changed to minimize self-absorption, were obtained and compared . The implication of all obtained results are discussed. 2. Background Theory 2.1. X-ray Fluorescence The process of XRF is realized through the shell model of the atom. This model consists of a series of electron orbits (or shells) surrounding an atomic nucleus as shown in Figure 1. The proximity of a particular shell to the atomic nucleus reflects how tightly bound the electrons it houses are to that nucleus. Thus the K-shell would then be the shell with the most tightly bound electrons. If an atom is excited from its ground state from an impinging photon via the photoelectric effect, the electrons would rearrange themselves to de-excite the atom re- sulting in the emission of a fluorescent X-ray photon [4]. To conserve momentum and energy, an incident photon is most likely to create a vacancy in the K-shell. Consequently, an electron from less bound shells (L, M etc) will be transferred to the vacancy emitting the fluorescent X-ray photon in the pro- cess with energy equal to the difference in binding energy be- tween the two shells. The possible origins of a fluorescent X- ray are illustrated in Figure 2 [4]. Competing with XRF is the Auger process which dominates for lower atomic number (z) atoms. This is where the atom de-excites through the emission of an outer shell electron as opposed to an X-ray photon [4]. Mosely’s law describes how the energy of the emitted fluo- rescent X-ray is proportional to Z2 with a proportionality con- stant that depends on the shells involved in the emission as shown in Figure 2. (Z is the atomic number of an element) More specifically the relationship for the K and L line’s X-ray frequency with Z is [8]: Kα : vx−ray ∼ (Z − 1) 2 (1) Figure 1. The Atomic shell structure. (http://earthsci.org/education/teacher/basicgeo/miner/electshells.gif) Figure 2. An illustration of possible sources of Fluorescent X-rays. Lα : vx−ray ∼ (Z − 7.4) 2 (2) The additional constants of 1 and 4.5 account for the screening effect from outer shell electrons on the fluorescent X-ray. The XRF is considered a powerful tool for identifying elemental composition in materials because of the X-ray’s energy strong dependence on the Z of its origin atom [8]. 2.2. Self-absorption and Secondary emission Self-absorption a frequent occurence in fluorescent X-ray spectroscopy is where X-rays produced from one atomic class in an alloy are absorbed by an atom of different atomic num- bers. Fernandez et al. [9] further studied this phenomenon and sought for a means of correcting the intensity of X-rays for sec- ondary emission. They suggested that the total intensity IT of a characteristic line from an atom is a combination of XRF from the ‘primary’ excitation source, I1 and the absorption of char- acteristic X-rays from other atoms which may then emit ‘sec- ondary’ X-rays, I2 [9]. Thus: IT = I1 + I2 (3) By considering the propagation plane of the incident and the fluoresced beam of photons as shown in Figure 3 the intensity of secondary emission dependence on the geometry can be ap- preciated. The effects of secondary emission can be removed by noting that I2 → 0 as the angle of the propagation plane α → 90o. 2 Etim & Mfon / J. Nig. Soc. Phys. Sci. 4 (2022) 926 3 Figure 3. Propagation plane of incident and take off X-rays varied with α [9 ]. Figure 4. The I2 probability bubble model for (c) α = 0o, (a) 0o < α < 90o and (b) α = 90o [9]. The mechanism of this process is described by a probability bubble by considering an infinitely long sample. Primary flu- orescent X-ray photons are produced at the very center of the sphere and travel isotropically across the radius of the bubble and are absorbed producing a subsequent secondary emission at the surface of the sphere. When α = 0o the position of the bubble is such that it is completely immersed in the material producing a large number of secondary photons which are emit- ted normal to the surface of the sample. Figure 4 shows that by increasing α, the probability bubbles begin to leave the material meaning that less secondary X-rays are produced. Figure 5 shows the results of a Monte Carlo simulation (with 50,000 photons) published by Fernandez et al. [9] which shows the relationship between the Intensity of secondary pho- tons as a function of angle α for a binary. Note how it falls to zero at 90o as in accordance with the probability bubble model. Throughout this process, the intensity of the primary photons remains invariant to α, hence when α = 90o, IT = I1 [9]. 2.3. Semiconductor Detectors When a photon impinges on a semiconductor detector, electron- hole pairs are produced. Electrons move from the valence band to the conduction band and due to the electric field across the detector, they move to the positive electrode. A hole that is pro- duced in the first position of the electron moves to the negative electrode. That charge created is measured across the detector. Figure 5. Secondary emission dependence on α from a Monte Carlo simulation developed in Pascal with 50,000 initial photons [9]. In this experiment, two different semiconductor detectors namely the Silicon (Si) and the Cadmium telluride (CdTe) de- tectors were used. In the Si detector, 3.6 eV is required to pro- duce one electron-hole (e/h) pair while in the CdTe detector, 4.43 eV is required [4, 10]. In both Amptek detectors used, there is a high voltage across them to help in the collection of the charge and produce an in- crease in their efficiency. Conversely because that voltage is high, the resolution of the detector reduces and the effect from leakage current becomes more significant. That is why a ther- moelectric cooler is installed just next to the detector and the pre-amplifier so that the electronic noise of the system is re- duced and the resolution of the detector is enhanced as the peaks seem narrower. Apart from the cooler, there is a small monitor to read the temperature directly and the Beryllium window is used for the low energy photons (X-rays) [10]. At the range of low X-rays energies that were measured in this experiment, the Si detector resolution was compared to that of the CdTe detec- tor. Thus the resolution of a peak given as a percentage is: Resolution(%) = FW H M Centroid × 100 (4) (where FWHM is the Full Width at Half Maximum of the peak and ‘Centroid’ is the centroid of the peak defined by the soft- ware). At that chosen energy range, the CdTe detector has an ex- tremely high efficiency. Thus to find the efficiency of the Si detector, which was assumed should be lower than that of the CdTe detector, the CdTe detector was assumed to be 100% ef- ficient and the ratio of the two intensities gives the efficiency of the Si detector[10]. The error in resolution can be calculated using Equation 5 : σR = R · √( σFW H M FW H M )2 + ( σCentroid Centroid )2 (5) 3 Etim & Mfon / J. Nig. Soc. Phys. Sci. 4 (2022) 926 4 Figure 6. Experimental Setup showing the copper collimator, lead shield and Detector. 3. Methodology 3.1. Materials An X-ray tube with an Air-cooled Mo K as a primary X-ray source was used. Si and CdTe detectors with gains 100 and 3 respectively were used. Other instruments included an Ampli- fier, a DP4 Digital pulse processor, a computer with software maestro which was used for data acquisition and samples stud- ied were single element metals and Alloys in plate form. 3.2. System geometric setup/Calibration of CdTe detector A copper sample was placed 30 cm from the X-ray source and the sample plate was turned at 45o to the primary X-ray beam. The detector was placed at 45o to the sample and 25 cm from it such that the angle between the X-ray beam and the detector axis is 90o. In this setup, there was no beam colli- mator nor a shield between the collimator and the detector and so the detector energy calibration was done using Americium- 241(241Am) .With the X-ray set at 50 kV, the sample was scanned for 500 s and a spectra was obtained. The spectra obtained had a large continuum background with no identifiable characteris- tic X-ray peaks and so another set up which was a modification of the first was created. A copper collimator was placed in front of the X-ray source to bring to a focus on a limited area of the target, the primary X- ray beam and prevent them from spreading to hit the material around the system instead of the target. Furthermore, a lead shield was placed between the collimator and the detector to prevent the secondary X-rays from the collimator getting to the detector. The distance between the X-ray source and the sample was reduced to 20 cm while that between the sample and the detector was 10 cm. The angle between the primary X-ray beam and the detector axis was maintained at 45o (Figure 6). With the X-ray source at 50 kV and for 500 s, another spectra of the calibration sample was obtained. The calibration plot is as shown in Figure 7. The spectra for single-element samples like copper and lead as well as for alloys (brass and steel) were obtained and anal- ysed. The effects of secondary emission from the sample were also investigated using Si detector as illustrated in Figure 3. With the brass sample placed in the sample holder such that the incident X-ray beam was normal to the plane and with a brass collimator in place, the spectra for copper after 500 seconds was obtained. For X-rays of intensity 8.048 keV, the characteristic X-ray peak for copper was obtained. This process was repeated for various values of α ranging from 0o to 90o. Using the same setup but without a sample, the background was measured and obtained results are presented in Table 2. Using the CdTe detector and the setup described above, the spectra of different samples were also collected in order to iden- tify their composition from their characteristic X-ray peaks. Obtained results are presented in Table 2. For the alloys, the ratio of their constituent elements was calculated by assuming that the amount of each element in the alloy sample is proportional to the number of counts in the peak of the characteristic lines of each element. The most abundant element was used as a reference to determine the abundance of the other constituent elements in the sample. As was done with the CdTe detector, the spectra of the same samples were analysed with the Si detector to get each sample composition. The resolution of the Si detector was measured and obtained results were compared with those for the CdTe detector. The efficiency of the Si detector was also calculated and the ratio of the Si/CdTe intensities was measured and plot- ted as a function of the theoretical photon energy. The error for the ratio was calculated using: σI = √√( σIS i ICdT e )2 +  IS i ·σICdT e I2CdT e 2 (6) The uncertainties for the intensities, of Si and CdTe detectors: σIS i = σICdT e = σN t (7) The error of the number of counts was found from the Poisson statistics. The theoretical energy assumed that it does not have an error. Furthermore, for the Brass sample, the effect of vary- ing the propagation plane angle α for the Cu 8.048 keV peak was also studied and the result is presented in Figure 12. 4. Results and Discussion The calibration plot for the CdTe detector performed using the Am source is shown in Figure 7. A first-order polynomial fit is visible above using the equation y = ax + b, where a = (0.017 ± 0.003) keV and b = (−0.061 ± 0.006) keV . The values and errors for a and b were calculated from the software “OriginPro8” using the least-squares method. The er- ror bars of the channel number are very small and therefore were not visible in the graph. The slope of the above plot gave the gain of the system as (0.017 ± 0.003) keV/channel. The CdTe detector resolution was calculated using the spec- trum for the calibration and Equation 4 and the error for each peak was calculated using Equation 5. Obtained results are as presented in Table 1. The errors were very small so more decimal places were introduced and the CdTe detector resolution was high at 0.38 % with the poorest resolution being 3.37 %. 4 Etim & Mfon / J. Nig. Soc. Phys. Sci. 4 (2022) 926 5 Figure 7. Theoretical Energy against the channel number (CdTe detector). Table 1. Energy resolution of the CdTe detector. Peak Energy Error in Energy (keV ) Resolution (%) Resolution (%) 8.01 0.38 0.0001 13.90 3.37 0.0013 17.70 2.04 0.0005 59.50 0.99 0.0001 The energy of the characteristic X-rays of each sample was measured using the Maestro software which translated the ob- tained results to the peak centroid energy. The uncertainty for the energy was calculated using the standard error in the mean. The energies of the XRF of the samples in all cases except for lead were derived from the main peaks found in the spectra due to Kα characteristic line. Kα X-rays from lead have higher energies when compared with the range of energies measured (∼ 79 keV ), hence only Lα and Lβ transition were seen in the spectrum and recorded in Table 2. Table 2 shows the characteristic X-ray energies, the errors as well as the percentage differences between the obtained val- ues and the published values for the other samples. The errors as in the first case are very small. For lead, more than one transition was presented and the X-rays used were of high intensity and they were easily distin- guished. The percentage difference was calculated using Equa- tion 8 : %Di f f erence =( EnergyT heoretical − Energymeasured EnergyT heoretical ) × 100 (8) The background measurements show two peaks which are present in all spectra. The first peak at 16.61 keV is for the XRF pro- duced from the X-ray tube. The X-ray tube is made of Mo and thus the visible peak in the spectrum has the energy of the Kα X-ray of Mo. Furthermore, in all spectra, a peak with energy Figure 8. Spectra of characteristic X-rays of Lead and Brass. 7.80 keV was found. That peak is due to the XRF produced from the collimator which is made of Copper. Consequently, samples with a small amount of copper were not measured as the peak from copper was seen as a background peak. For the brass sample, the most abundant element is Cop- per. With this as the reference, the ratio of the counts for Zn peak to the counts of the Cu peak was calculated and found to be 1:0.25. By the same reasoning, for steel, the main element is iron (Fe) but Nikel(Ni) and Copper (Cu) are also available. Thus the ratio of Fe : Ni : Cu was found to be 1:0.20:0.03. The spectra showing the characteristic fluorescent X-rays for steel and Brass are shown in Figure 8. 4.1. Silicon (Si ) detector calibration plot The calibration plot for the Si detector is as shown in Fig- ure 9. A first-order polynomial fit is visible above using the equation y = ax + b, where a = (0.038 ± 0.002) keV and b = (−0.064 ± 0.002) keV . The values and errors for a and b were calculated from the software “OriginPro8” using the least-squares method. The er- ror bars of the channel number are very small and therefore not visible in the graph. The slope of the above plot gave the gain of the system which was (0.038±0.002) keV/channel. The energy resolution of the Si detector was measured and are as presented in Table 3. 5 Etim & Mfon / J. Nig. Soc. Phys. Sci. 4 (2022) 926 6 Figure 9. Calibration plot of the Silicon Detector. Table 3. Energy resolution of the Si detector. Peak Energy Error in Energy (keV ) Resolution (%) Resolution (%) 13.90 4.29 0.0014 17.70 3.62 0.0010 59.50 0.27 0.0000 The errors for the Si detector as in the case of CdTe were very small so more decimal numbers were used in order to give a more accurate value. The peaks measured from the background were the same peaks found when the CdTe detector was used. A comparison of the energy resolution of the Si detector (Table 3) with that of the CdTe detector (Table 1) shows that the resolution of the Si detector is lower. That was strange because at lower energy ranges, the Si detector has a higher resolution compared with the CdTe detector. This discrepancy was attributed to the noisy amplifier which may have reduced the resolution of the system. As before, the errors were very small so more decimal numbers were introduced. The ratio of the elements in Brass, Cu:Zn was found to be 1:0.70. For the steel, as it is shown from Table 4, one peak was visible so the ratio of the different elements could not be calculated. This perhaps was due to the lower resolution of the Si detector using that amplifier. For a visible difference in the resolution of the Si detector, another amplifier was used (with shaping time equal to 12 µs). A new calibration plot (Figure 10) was done for the Si detector with the new amplifier and the obtained results were found to be completely different. A first-order polynomial fit is visible above using the equa- tion y = ax + b, where a = (0.014 ± 0.003) keV and b = (0.014±0.001) keV . The values and errors for a and b were cal- culated as above. The error bars of the channel number are very Figure 10. New calibration plot for Si detector used with new amplifier. Figure 11. Silicon detector efficiency relative to CdTe detector. Figure 12. Total Intensity dependence on α for a Cu 8.048 keV peak. small and therefore cannot be visible in the graph. The slope of the above chart gives the gain of the system. Therefore, it can be seen that the gain is equal to (0.014 ± 0.003) keV/channel. The resolution was then calculated and compared with the previous one (Table 5). 6 Etim & Mfon / J. Nig. Soc. Phys. Sci. 4 (2022) 926 7 Table 4. Showing the sample composition and identified elements with their characteristic X-ray energies and associated uncertainties for Si detector Sample Element Characteristic Uncertainty Published Percentage X-ray energy of the X-ray X-ray difference (keV) Energy (keV) Energy (keV) Background Mo 16.41 0.00319 17.479 6.116 Cu 7.44 0.00681 8.048 7.555 Copper Cu 8.00 0.00009 8.048 0.596 Mo Mo 17.33 0.00029 17.479 0.852 Lead Pb 14.73 0.00093 14.765 0.237 Pb 12.53 0.00026 12.614 0.666 Pb 10.48 0.00067 10.551 0.673 Brass Cu 7.96 0.00014 8.048 1.093 Zn 8.57 0.00013 8.639 0.799 Steel Fe 8.53 0.00012 6.404 33.198 Ni 8.53 0.00012 7.478 14.068 Cu 8.53 0.00012 8.048 5.989 Table 5. New energy resolution for Si detector with new amplifier Peak Energy Energy Error in New Resolution Error in New (keV) Resolution (%) Resolution (%) (%) Resolution (%) 13.90 4.29 0.0014 2.13 0.0005 17.70 3.62 0.0010 1.65 0.0004 59.50 0.27 0.0001 0.04 0.0001 Table 6. Showing the new sample composition for Brass and Steel with their characteristic X-ray energies and associated uncertainties for Si detector with new amplifier Sample Element Characteristic Uncertainty Published Percentage X-ray energy of the X-ray X-ray difference (keV) Energy (keV) Energy (keV) Brass Cu 6.29 0.00066 6.404 1.780 Zn 8.61 0.00037 8.048 6.983 Fe 8.00 0.00037 6.404 1.780 Steel Cu 7.98 0.00464 8.048 0.845 Ni 7.01 0.00084 7.478 6.258 Fe 6.36 0.00032 6.404 0.687 With the new amplifier, a higher resolution of the Si detec- tor was obtained from the new spectra produced. For the errors as before were very small and so more decimal numbers were used in order to give a more accurate. To test how efficient the Si detector was with new amplifier, the spectra for brass and steel were acquired and the results are displayed in Table 6. The errors were small and the peaks were easily distinguished. The ratios of the constituent elements in these two Alloys were cal- culated and for Brass, a peak due to iron (Fe) though of a lower intensity could be distinguished because now the detector reso- lution was higher (recall that with the CdTe detector that peak was not visible). The ratio Cu:Zn:Fe in Brass was found to be 1:0.53:0.01 while the ratio Fe:Ni:Cu for Steel was 1:0.14:0.01. The efficiency of the CdTe detector was assumed to be 100% and thus the ratio of the intensities gives the efficiency of the Si detector and high energies were found to produce lower detec- tor efficiencies. This is because photons with higher energies move faster in the detector and intereact less with the sample so the number of counts measured is less and resulted in a lower efficiency. The graph which shows the total number of counts from flu- orescent X-rays in the 8.048 keV Cu characteristic X-ray peak of the brass sample for different inclination angles α shows that the intensity decreases as α increases suggesting a reduction in the enhancement from self-absorption and secondary X-ray emission as predicted by Fernandez’s bubble model. For this data to correctly fit the model, the photons from the X-ray tube have to be heavily collimated to produce a thin beam. The Monte Carlo simulation results in Figure 5 was pro- duced from modeling a point beam but the same level of colli- mation could not be achieved experimentally as the risk of no XRF hitting the detector at all and also the scattering continuum would dwarf any characteristic X-ray peaks present. Moreover, the model assumes an infinitely long and thick sample, although 7 Etim & Mfon / J. Nig. Soc. Phys. Sci. 4 (2022) 926 8 due to the probabilistic nature of photon, not all the X-rays will be absorbed, and the sample thickness will have a direct conse- quence on the number of counts. 5. Conclusion This project developed a means of non-destructively deter- mining the composition of metals through a study of the energy of their emitted characteristic X-rays. A Mo source X-ray tube collimated to scatter off a sample at a 45o incidence and take- off angle to a semiconductor detector was used. The intensity of the characteristic X-ray energy peaks from different samples was used for estimating the abundance of particular elements in each sample. The silicon detector superior resolution over that of the CdTe detector proved to be a much better tool for correctly identify- ing energy peaks. However, its reduced efficiency translated to poor counting statistics at higher energies as seen from the re- duced energy resolution for a 241 Am γ − peak at 59.5 keV for the silicon detector. Thus higher energies were found to pro- duce lower detector efficiencies. The peak intensities from steel and brass alloys were used to estimate element composition and these produced reasonable abundances of zinc compared to copper. The investigation into the correction of secondary emission was done using the ‘prob- ability bubble’ model described by Fernandez et al. [9]. Exper- imentally the dependence on total intensity on the angle α com- pares well with the model. The limiting factors in this technique however lie in the level of collimation that can be placed on the beam without reducing counting statistics to an unacceptable level and preventing the scattering component from dwarfing any characteristic lines present. To extend this study, it might be necessary to develop a setup that can measure the angle α much more accurately. 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