Incomplete Charge Collection at Inter-Pixel Gap in Low- and High-Flux Cadmium Zinc Telluride Pixel Detectors

The success of cadmium zinc telluride (CZT) detectors in room-temperature spectroscopic X-ray imaging is now widely accepted. The most common CZT detectors are characterized by enhanced-charge transport properties of electrons, with mobility-lifetime products μeτe > 10−2 cm2/V and μhτh > 10−5 cm2/V. These materials, typically termed low-flux LF-CZT, are successfully used for thick electron-sensing detectors and in low-flux conditions. Recently, new CZT materials with hole mobility-lifetime product enhancements (μhτh > 10−4 cm2/V and μeτe > 10−3 cm2/V) have been fabricated for high-flux measurements (high-flux HF-CZT detectors). In this work, we will present the performance and charge-sharing properties of sub-millimeter CZT pixel detectors based on LF-CZT and HF-CZT crystals. Experimental results from the measurement of energy spectra after charge-sharing addition (CSA) and from 2D X-ray mapping highlight the better charge-collection properties of HF-CZT detectors near the inter-pixel gaps. The successful mitigation of the effects of incomplete charge collection after CSA was also performed through original charge-sharing correction techniques. These activities exist in the framework of international collaboration on the development of energy-resolved X-ray scanners for medical applications and non-destructive testing in the food industry.

As is well known, the most important critical issues in sub-millimeter CZT pixel detectors are represented by charge-sharing and crosstalk effects, with the presence of severe degradations in both the spectral and spatial performance [29][30][31][32][33][34][35][36][37][38][39][40]. Despite the potential of charge-sharing addition (CSA) techniques in reducing the charge-sharing effects, the presence of incomplete charge collection in the summed energy after CSA often prevents full energy recovery in the energy spectra [33][34][35][36][37][38][39][40]. These effects, due to the presence of charge losses at the inter-pixel gaps, are strictly related to the physical properties of the detectors (crystals and electrical contacts) near the gaps between the pixels.
In this work, we investigated the effects of charge losses near the inter-pixel gap in LF/HF-THM CZT pixel detectors. The detectors are fabricated on THM-CZT crystals recently produced by Redlen Technologies company (Canada), for both low-(LF-CZT) [19][20][21][22] and high-(HF-CZT) flux applications [27][28][29]. Measurements with uncollimated radiation sources and collimated synchrotron X-ray beams were performed on LF/HF-CZT pixel detectors characterized by the same crystal dimensions, electrical layout, bias voltage operation, and readout electronics.

The CZT Pixel Detectors
Two-millimeter-thick CZT pixel detectors characterized by the same electrode layout and dimensions (4.25 × 3.25 × 2 mm 3 ) were investigated. Regarding the electrode layout ( Figure 1), all anodes consist of four arrays of 3 × 3 pixels: a large array with a pixel pitch of 500 µm and three small arrays with pixel pitches of 250 µm.
Sensors 2022, 22, x FOR PEER REVIEW greater than 10 −2 cm 2 /V, was pioneered by Chen in 2007 [21]. Since then, several sup (Redlen Technologies, Canada; Kromek, UK) were able to fabricate high-μeτe CZT c with thicknesses greater than 10 mm. Excellent performances were obtained in thic detectors (>5 mm), where the particular electron-sensing design (a drift strip and co grids) is often optimized to work in low-electricity fields (<1000 V/cm) [8,9]. Beside great efforts have also been made to enhance the mobility-lifetime products of the (μhτh), especially for high-flux measurements. Enhancements in hole charge tra properties are necessary to minimize the effects of radiation-induced polarizatio nomena at high fluxes [23][24][25][26]. Recently, high-μhτh THM-CZT crystals (μhτh > 10 −4 c are provided by Redlen for high-flux applications [27][28][29]. Therefore, high-μhτh CZ tectors (high-flux HF-CZT detectors) are typically used for high-flux measurements high-μeτe CZT materials (low flux LF-CZT) for thick electron-sensing detectors gen work at low flux conditions.
As is well known, the most important critical issues in sub-millimeter CZT pi tectors are represented by charge-sharing and crosstalk effects, with the presence of degradations in both the spectral and spatial performance [29][30][31][32][33][34][35][36][37][38][39][40]. Despite the po of charge-sharing addition (CSA) techniques in reducing the charge-sharing effec presence of incomplete charge collection in the summed energy after CSA often pr full energy recovery in the energy spectra [33][34][35][36][37][38][39][40]. These effects, due to the prese charge losses at the inter-pixel gaps, are strictly related to the physical properties detectors (crystals and electrical contacts) near the gaps between the pixels.
In this work, we investigated the effects of charge losses near the inter-pixel LF/HF-THM CZT pixel detectors. The detectors are fabricated on THM-CZT cryst cently produced by Redlen Technologies company (Canada), for both low-(LF- CZT 22] and high-(HF-CZT) flux applications [27][28][29]. Measurements with uncollimate ation sources and collimated synchrotron X-ray beams were performed on LF/H pixel detectors characterized by the same crystal dimensions, electrical layout, bia age operation, and readout electronics.

The CZT Pixel Detectors
Two-millimeter-thick CZT pixel detectors characterized by the same electrode and dimensions (4.25 × 3.25 × 2 mm 3 ) were investigated. Regarding the electrode (Figure 1), all anodes consist of four arrays of 3 × 3 pixels: a large array with a pixe of 500 µ m and three small arrays with pixel pitches of 250 µ m.  The cathode is a simple planar electrode covering the surface of the detectors. All arrays are designed with the same inter-pixel gap of 50 µm. The detectors are based on lowflux LF-THM CZT and high-flux HF-THM CZT crystals, developed by Redlen Technologies (Canada).

Hih Flux HF-CZT Detectors
The HF-CZT pixel detectors were fabricated by Redlen Technologies with platinum electrical contacts. The charge transport properties are represented by µ e τ e ranging from 2 to 3 ×10 −3 cm 2 /V and µ h τ h from 1 to 2 ×10 −4 cm 2 /V [27].

Readout Electronics
The processing of the detector signals was performed using the same readout electronics for all detectors. Regarding the front-end electronics, the detectors were flip-chip bonded to charge-sensitive preamplifiers (CSPs) based on a low-noise application-specific integrated circuit (PIXIE ASIC) developed at RAL (Didcot, UK) [42]. The PIXIE ASIC, characterized by an equivalent noise charge (ENC) less than 80 electrons, provides nine output channels at the same time for each 3 × 3 pixel array. The output waveforms from the PIXIE ASIC are digitized and processed online by 16-channel digital electronics, developed at DiFC of the University of Palermo (Italy) [35,36,43,44]. The digital electronic is based on commercial digitizers (DT5724, 16-bit, 100 MS/s, CAEN SpA, Italy), where an original firmware was uploaded [43,44].

Spectroscopic Performance
The spectroscopic response of the detectors, when illuminated with uncollimated radiation sources ( 109 Cd, 241 Am, 57 Co), was measured. The detectors, biased at 1000 V (5000 V/cm), are characterized by a similar room-temperature performance (T = 20 • C), as shown in Figure 2. This bias voltage value represents, for both detectors, the optimum setting for the best energy resolution. The energy resolution (FWHM) of both detectors is from less than 2 keV up to 122 keV. The similar performance of the detectors, despite the different charge transport properties of the CZT crystals, is due to several factors, e.g., the high-bias voltage operation, the small thickness, and the electron-sensing properties of the pixel detectors. In this last case, the fluorescent X-rays create both an increase in the charge cloud dimensions and the generation of crosstalk phenomena between the pixels. Regarding the coincidence percentages, the results for the central pixel show values of 33-34% and 52-53% at 22.1 keV for the 500 µ m and 250 µ m arrays, respectively; while at energies greater than the K-shell absorption energy, we measured values of 56-58% and 79-81% at 59.5 keV for the 500 µ m and 250 µ m arrays, respectively. Figure 3 shows a comparison between the raw energy spectrum of the central pixel of the large 500 μm array (black line) and the spectrum with only single events (violet line), i.e., the events with multiplicity m= 1. The shape of the energy spectrum is strongly improved after the rejection of the coincidence events, i.e., after the application of the charge-sharing discrimination (CSD) technique. The coincidence events are mainly a result of charge-sharing and fluorescence crosstalk phenomena, and their effects are clearly visible in the raw spectrum: The fluorescent peaks at 23.2 and 27.5 keV, the escape peaks at 36.3 and 32 keV, the low-energy background, and tailing. As is well known, a typical recovery of the rejected events after CSD can be performed through the classical charge-sharing addition (CSA) technique. Figure 4 shows the results obtained after the application of CSA in LF/HF-CZT detectors, at energies below ( 109 Cd source) and above ( 241 Am source) the K-shell absorption energy of CZT. Both detectors are characterized by energy deficits in the spectra after CSA (brown lines), particularly of about 3.1 keV (6 keV) and 1.6 keV (3 keV) at 22.1 keV (59.5 keV) for the LF and HF CZT detectors, respectively. We also observed that this energy deficit is strongly related to the bias voltage, e.g., at 500 V, we measured a deficit of about 9 keV and 5 keV at 59.5 keV for the LF and HF detectors, respectively. Moreover, the distribution of these energy deficits within the inter-pixel gap between two pixels is also presented in Figure 5. The two-dimensional (2D) scatter plots show the summed energy ECSA of the coincidence events (m = 2) between two adjacent pixels (pixels no. 5 and no. 6), after CSA, versus the charge-sharing ratio R. The quantity R, calculated from the ratio between the energies of two adjacent pixels ( Figure 5), gives indications about the position of the photon interaction between the two pixels.

Incomplete Charge Collection in Charge-Sharing Events
Charge-sharing measurements were performed through time coincidence analysis, with a particular focus on the coincidence events of the central pixel of each array with the neighboring pixels. The coincidence events were detected within a coincidence time window (CTW) of 200 ns, ensuring the full detection of all coincidence events. The number of coincidence events is the same for both detectors, confirming its dependence on the detector layout geometry. The percentage of the coincidence events is very high, and this number increases for high values of the ratio between the inter-pixel gap area and the pixel area and for energies greater than the K-shell absorption energy of the CZT material (26.7 keV, 9.7 keV, and 31.8 keV for Cd, Zn, and Te, respectively).
In this last case, the fluorescent X-rays create both an increase in the charge cloud dimensions and the generation of crosstalk phenomena between the pixels. Regarding the coincidence percentages, the results for the central pixel show values of 33-34% and 52-53% at 22.1 keV for the 500 µm and 250 µm arrays, respectively; while at energies greater than the K-shell absorption energy, we measured values of 56-58% and 79-81% at 59.5 keV for the 500 µm and 250 µm arrays, respectively. Figure 3 shows a comparison between the raw energy spectrum of the central pixel of the large 500 µm array (black line) and the spectrum with only single events (violet line), i.e., the events with multiplicity m= 1. The shape of the energy spectrum is strongly improved after the rejection of the coincidence events, i.e., after the application of the charge-sharing discrimination (CSD) technique. The coincidence events are mainly a result of charge-sharing and fluorescence crosstalk phenomena, and their effects are clearly visible in the raw spectrum: The fluorescent peaks at 23.2 and 27.5 keV, the escape peaks at 36.3 and 32 keV, the low-energy background, and tailing. As is well known, a typical recovery of the rejected events after CSD can be performed through the classical charge-sharing addition (CSA) technique. Figure 4 shows the results obtained after the application of CSA in LF/HF-CZT detectors, at energies below ( 109 Cd source) and above ( 241 Am source) the K-shell absorption energy of CZT. Both detectors are characterized by energy deficits in the spectra after CSA (brown lines), particularly of about 3.1 keV (6 keV) and 1.6 keV (3 keV) at 22.1 keV (59.5 keV) for the LF and HF CZT detectors, respectively. We also observed that this energy deficit is strongly related to the bias voltage, e.g., at 500 V, we measured a deficit of about 9 keV and 5 keV at 59.5 keV for the LF and HF detectors, respectively. Moreover, the distribution of these energy deficits within the inter-pixel gap between two pixels is also presented in Figure 5. The two-dimensional (2D) scatter plots show the summed energy E CSA of the coincidence events (m = 2) between two adjacent pixels (pixels no. 5 and no. 6), after CSA, versus the charge-sharing ratio R. The quantity R, calculated from the ratio between the energies of two adjacent pixels ( Figure 5), gives indications about the position of the photon interaction between the two pixels.   The curvature shows the presence of energy deficits for both detectors and at all energies; they are more severe at R = 0, i.e., related to events interacting at the center of the inter-pixel gap. The summed energy E CSA of certain coincidence events at about R = 0.22 is fully recovered after CSA. These events represent the coupling of fluorescent X-rays at 23.2 keV and the escape events at 36.3 keV. As is clearly shown in Figures 4 and 5, the energy deficit after CSA is less severe for the HF-CZT detectors. Recently, similar results were obtained by other researchers [29]; in particular, they measured less-incomplete charge collection after CSA in HF-CZT pixel detectors, in comparison with CdTe pixel detectors, attributing this to the better hole transport properties of the HF-CZT crystals than the CdTe ones. We believe that this difference is not dependent on the charge transport properties of the carriers but is strictly related to the characteristics of the electric field lines near the inter-pixel gaps. To confirm this conclusion, we also measured the energy deficits in chargesharing events, where the charge clouds are mainly contributed to by the electrons; in this case, because of the better electron charge transport properties of the LF-CZT detectors than the HF-CZT ones, the charge losses in LF-CZT detectors should be less severe than the HF-CZT ones. In order to investigate shared events with high electron contributions in the charge cloud, we used low-energy X-rays (22.1 keV X-rays from the 109 Cd source) interacting near the cathode side and measured the events from the pixels of the 250 µm arrays, characterized by high electron-sensing properties (in agreement with the small pixel effect [2]). The results are presented in Figure 6.
The energy deficits of the 22.1 keV photopeaks after CSA are approximately 3.5 keV and 2.5 keV for the LF-CZT and HF-CT detectors, respectively; the degradation continues to be more severe for the LF-CZT detector, confirming that the charge losses are not related to the transport properties of the charge carriers. This was also confirmed by simulation procedures. We performed a simulation of the two-dimensional (2D) scatter plots of the summed energy E CSA of the coincidence events (m = 2) between two adjacent pixels, for both detectors and arrays. The simulations were carried out by means of a first principle tool [45], composed of three main blocks: (i) The radiation-semiconductor interaction based on the Monte Carlo approach (Geant4), (ii) electric and weighting field calculation by the finite element method (FEM) with COMSOL Multiphysics, and (iii) the computation of the charge carrier transport and pulse formation in the MATLAB environment. In order to evaluate whether the charge losses in LF/HF CZT detectors are due to the transport properties of carriers, a spatially homogeneous distribution of charges was simulated inside the whole CZT volume. To focus the attention on the transport properties, any crystal defects (e.g., Te inclusions) or inter-pixel electric field distortions were implemented in simulations. The simulation was carried out using the physical quantities reported in Table 1.     The curvature shows the presence of energy deficits for both detectors and at all energies; they are more severe at R = 0, i.e., related to events interacting at the center of the inter-pixel gap. The summed energy ECSA of certain coincidence events at about R = 0.22 is fully recovered after CSA. These events represent the coupling of fluorescent X-rays at 23.2 keV and the escape events at 36.3 keV. As is clearly shown in Figures 4 and 5, the energy deficit after CSA is less severe for the HF-CZT detectors. Recently, similar results were obtained by other researchers [29]; in particular, they measured less-incomplete charge collection after CSA in HF-CZT pixel detectors, in comparison with CdTe pixel detectors, attributing this to the better hole transport properties of the HF-CZT crystals than the CdTe ones. We believe that this difference is not dependent on the charge transport properties of the carriers but is strictly related to the characteristics of the electric field lines near the inter-pixel gaps. To confirm this conclusion, we also measured the energy deficits in charge-sharing events, where the charge clouds are mainly contributed to by the electrons; in this case, because of the better electron charge transport properties of the LF-CZT detectors than the HF-CZT ones, the charge losses in LF-CZT detectors should be less severe than the HF-CZT ones. In order to investigate shared events with high electron contributions in the charge cloud, we used low-energy X-rays (22.1 keV X-rays from the 109 Cd source) interacting near the cathode side and measured the events from the pixels of the 250 μm arrays, characterized by high electron-sensing properties (in agreement with the small pixel effect [2]). The results are presented in Figure 6. The energy deficits of the 22.1 keV photopeaks after CSA are approximately 3.5 keV and 2.5 keV for the LF-CZT and HF-CT detectors, respectively; the degradation continues to be more severe for the LF-CZT detector, confirming that the charge losses are not related to the transport properties of the charge carriers. This was also confirmed by simulation procedures. We performed a simulation of the two-dimensional (2D) scatter plots We simulated the two-dimensional (2D) scatter plots of the summed energy E CSA of the coincidence events (m = 2) between two adjacent pixels, after CSA, versus the chargesharing ratio R, for both detectors and arrays (Figure 7). No remarkable differences are present in the comparison of the charge losses. This means that transport properties do not significantly influence the charge loss mechanism. These effects are due to the presence of distortions and non-uniformities in the electric field lines near the gaps between the pixels. This was also confirmed by the results obtained after a micro-scale 2-D X-ray mapping of the detectors. Collimated synchrotron X-ray beams were used at the B16 test beamline at the Diamond Light Source facility (Didcot, UK), in particular, 10 x 10 μm 2 micro-beams with scan steps of 12.5 μm at 40 keV. The results of the mapping for the small 250 μm arrays are shown in Figure 8, where the 40 keV photopeak energy at different positions is presented.  These effects are due to the presence of distortions and non-uniformities in the electric field lines near the gaps between the pixels. This was also confirmed by the results obtained after a micro-scale 2-D X-ray mapping of the detectors. Collimated synchrotron X-ray beams were used at the B16 test beamline at the Diamond Light Source facility (Didcot, UK), in particular, 10 × 10 µm 2 micro-beams with scan steps of 12.5 µm at 40 keV. The results of the mapping for the small 250 µm arrays are shown in Figure 8, where the 40 keV photopeak energy at different positions is presented.
Both detectors, due to the charge sharing, show a reduction in the photopeak energy near the inter-pixel gaps; however, the LF-CZT detector is characterized by an extended charge-sharing region (blue region), due to the increased presence of distortions and nonuniformities in the electric field lines. The cause of these distortions is unclear but may be due to either the presence of crystalline defects (inclusions) or perhaps issues with the electrical contacts. Fortunately, the energy deficits of the shared events after CSA can be recovered through a custom correction technique, recently developed by our group [36,37]. This technique is based on the correction of (i) the shared events after CSA with m = 2, (ii) the events with m > 2, and (iii) the fluorescence crosstalk events. The results after charge-sharing correction (CSC) for both LF/HF-CZT detectors are presented in Figure 9.
These effects are due to the presence of distortions and non-uniformities in the electric field lines near the gaps between the pixels. This was also confirmed by the results obtained after a micro-scale 2-D X-ray mapping of the detectors. Collimated synchrotron X-ray beams were used at the B16 test beamline at the Diamond Light Source facility (Didcot, UK), in particular, 10 x 10 μm 2 micro-beams with scan steps of 12.5 μm at 40 keV. The results of the mapping for the small 250 μm arrays are shown in Figure 8, where the 40 keV photopeak energy at different positions is presented.  Both detectors, due to the charge sharing, show a reduction in the photopeak energy near the inter-pixel gaps; however, the LF-CZT detector is characterized by an extended charge-sharing region (blue region), due to the increased presence of distortions and nonuniformities in the electric field lines. The cause of these distortions is unclear but may be due to either the presence of crystalline defects (inclusions) or perhaps issues with the electrical contacts. Fortunately, the energy deficits of the shared events after CSA can be recovered through a custom correction technique, recently developed by our group [36,37]. This technique is based on the correction of (i) the shared events after CSA with m = 2, (ii) the events with m > 2, and (iii) the fluorescence crosstalk events. The results after charge-sharing correction (CSC) for both LF/HF-CZT detectors are presented in Figure 9. As is clearly shown, the shared events are aptly detected and corrected in both detectors. However, while the raw and corrected spectra for the LF-CZT detector have the same energy resolution (1.8 keV FWHM at 59.5 keV), improvements in the energy resolution (1.4 keV versus 1.8 keV FWHM at 59.5 keV) characterize the corrected spectra for the HF-CZT detector. This result highlights the better collection properties of the HF-CZT detectors near the gaps between the pixels. As is clearly shown, the shared events are aptly detected and corrected in both detectors. However, while the raw and corrected spectra for the LF-CZT detector have the same energy resolution (1.8 keV FWHM at 59.5 keV), improvements in the energy resolution (1.4 keV versus 1.8 keV FWHM at 59.5 keV) characterize the corrected spectra for the HF-CZT detector. This result highlights the better collection properties of the HF-CZT detectors near the gaps between the pixels.

Conclusions
The spectroscopic performance and the charge-sharing properties of low-flux LF-THM CZT and high-flux HF-THM CZT pixel detectors are presented. The detectors, characterized by the same geometrical layout, allow high-bias voltage operation (5000 V/cm) and similar performances, with interesting room-temperature energy resolutions from <2 keV FWHM up to 122 keV. Despite the same charge-sharing percentages between the pixels, different charge-collection properties in sharing events are observed, highlighted by the presence of different energy deficits in the spectra after CSA. The HF-CZT detectors show fewer energy deficits after CSA, due to their better charge-collection properties near the inter-pixel gap, as confirmed by the micro-scale X-ray mapping. These results can be justified by the presence of a better electric field line distribution near the inter-pixel gap in HF-CZT detectors. Finally, the result of our successful correction of these energy deficits in both detectors is presented. This shows dramatic improvements in both the energy recovery and the energy resolution for HF-CZT pixel detectors.