Energy Recovery of Multiple Charge Sharing Events in Room Temperature Semiconductor Pixel Detectors

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Article Energy Recovery of Multiple Charge Sharing Events in Room Temperature Semiconductor Pixel Detectors

Antonino Buttacavoli 1, Gaetano Gerardi 1, Fabio Principato 1 , Marcello Mirabello 1, Donato Cascio 1 , Giuseppe Raso 1, Manuele Bettelli 2 , Andrea Zappettini 2 , Paul Seller 3, Matthew C. Veale 3 and Leonardo Abbene 1,*

1 Department of Physics and Chemistry (DiFC)-Emilio Segrè, University of Palermo, Viale delle Scienze, Ediﬁcio 18, 90128 Palermo, Italy; [email protected] (A.B.); [email protected] (G.G.); [email protected] (F.P.); [email protected] (M.M.); [email protected] (D.C.); [email protected] (G.R.) 2 IMEM/CNR, Parco Area delle Scienze 37/A, 43100 Parma, Italy; [email protected] (M.B.); [email protected] (A.Z.) 3 Science and Technology Facilities Council, Rutherford Appleton Laboratory, Chilton OX11 0QX, UK; [email protected] (P.S.); [email protected] (M.C.V.) * Correspondence: [email protected]

Abstract: Multiple coincidence events from charge-sharing and ﬂuorescent cross-talk are typical drawbacks in room-temperature semiconductor pixel detectors. The mitigation of these distortions in the measured energy spectra, using charge-sharing discrimination (CSD) and charge-sharing addition (CSA) techniques, is always a trade-off between counting efﬁciency and energy resolution. The energy recovery of multiple coincidence events is still challenging due to the presence of charge losses after Citation: Buttacavoli, A.; Gerardi, G.; CSA. In this work, we will present original techniques able to correct charge losses after CSA even Principato, F.; Mirabello, M.; Cascio, when multiple pixels are involved. Sub-millimeter cadmium–zinc–telluride (CdZnTe or CZT) pixel D.; Raso, G.; Bettelli, M.; Zappettini, detectors were investigated with both uncollimated radiation sources and collimated synchrotron X A.; Seller, P.; Veale, M.C.; et al. Energy rays, at energies below and above the K-shell absorption energy of the CZT material. These activities Recovery of Multiple Charge Sharing are in the framework of an international collaboration on the development of energy-resolved photon Events in Room Temperature counting (ERPC) systems for spectroscopic X-ray imaging up to 150 keV. Semiconductor Pixel Detectors. Sensors 2021, 21, 3669. https:// Keywords: CZT pixel detectors; charge sharing; charge-sharing correction; semiconductor pixel detectors doi.org/10.3390/s21113669

Academic Editor: Ming-Jie Sun

Received: 31 March 2021 1. Introduction Accepted: 23 May 2021 A large variety of room temperature semiconductor detectors (RTSDs) with sub- Published: 25 May 2021 millimeter pixel electrodes was widely proposed for the next generation X-ray and gamma ray spectroscopic imagers [1–6]. Generally, RTSDs are represented by X-ray and gamma ray Publisher’s Note: MDPI stays neutral detectors based on high-Z and wide-bandgap compound semiconductors, with the goal to with regard to jurisdictional claims in measure high-resolution energy spectra near room-temperature conditions. Currently, thin published maps and institutional afﬁl- cadmium telluride (CdTe) and cadmium–zinc–telluride (CdZnTe or CZT) pixel detectors, iations. with thickness up to 3 mm are considered the best choice up to 150 keV [7,8], while thicker detectors (up to 15 mm), based on CZT [9–12] and thallium bromide (TlBr) [13], are very appealing up to 1 MeV. RTSDs with small pixels represent a key choice for energy resolution improvements, which is in agreement with the small pixel effect [7] and potentially to obtain Copyright: © 2021 by the authors. high spatial resolution. However, the presence of multiple coincidence events among Licensee MDPI, Basel, Switzerland. neighboring pixels, due to charge-sharing and cross-talk phenomena [14–16], often results This article is an open access article in spectroscopic and spatial degradations. A single interacting photon can induce charges distributed under the terms and in two or more pixels, generating multiple coincidence events with multiplicity m ≥ 2. conditions of the Creative Commons Typically, the energy of these events is recovered by using charge-sharing addition (CSA) Attribution (CC BY) license (https:// techniques, which consist of summing the energies of the coincidence events. However, as creativecommons.org/licenses/by/ widely shown in both CdTe and CZT pixel detectors, charge losses at the inter-pixel gap 4.0/).

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often create incomplete energy recovery after CSA [17–19]. Recently, an energy-recovery technique for double charge shared events (m = 2) was proposed by our group [20] and successfully applied to several CZT and CdTe pixel detectors [20–25]. Despite the beneﬁts on detector performance, this technique can only be applied to shared events involving only two adjacent pixels (m = 2) and, therefore, multiple coincidences with m > 2 and coincidences with diagonal pixels are rejected from the measured energy spectra. In order to recover the energy of multiple coincidence events and enhance the counting efﬁciency, we developed new correction techniques able to use all coincidence events in the measured energy spectra. In this work, we will present new energy-recovery techniques for charge loss compen- sation after the application of CSA in CZT pixel detectors. Experimental investigations, taking into account the multiplicity of the coincidence events, were performed with both uncollimated and collimated synchrotron X-ray sources.

2. Charge-Sharing, Cross-Talk Phenomena and Correction Techniques Intense investigations have been made on the effects of charge-sharing and cross-talk phenomena in CZT and CdTe pixel detectors [14–25]. Charge-sharing events are generated by the splitting of the charge cloud created by a single interacting event and collected by two or more pixels. The charge cloud collected by pixels is mainly due to the drifting electrons, which is in agreement with the small pixel effect [7]. The spatial region covered by the broadened electron cloud depends upon charge diffusion, Coulomb charge repulsion, K- shell X-ray fluorescence, and Compton scattering. Figure1 shows the simulated evolution of the electron charge cloud size (FWHM) in a CZT detector vs. the drift distance, which is generated by photoelectrons in the energy range of 25–662 keV. The simulation involves the physical processes of Coulomb repulsion and charge diffusion [26]. It consists of three main procedures: (i) the radiation–semiconductor interaction with Monte Carlo methods (Geant4), (ii) electric and weighting field calculation by the finite element method (FEM) with COMSOL Multiphysics, and (iii) the calculation of the charge carrier transport and pulse formation in a MATLAB environment. The details of the simulation procedures are reported in a previous work [26]. The results are presented at two different electric field configurations: (a) 5000 V/cm representing the current state-of-art electric field in CZT detectors, while (b) the electric field of 10,000 V/cm was recently obtained in new high-bias voltage CZT pixel detectors [23,27]. For example, at 60 keV, the size of the charge cloud is about 60 µm and 45 µm over a drift distance of 2 mm, with 5000 V/cm and 10,000 V/cm, respectively. At energies greater than the K-shell absorption energy of the CZT material (26.7, 9.7, and 31.8 keV for Cd, Zn, and Te, respectively), the broadening of the charge cloud size can be also increased by the presence of fluorescent X rays, whose emission probability is very high in CZT materials (≈85% of all photoelectric absorptions) [25,28]. The emission of fluorescent X rays of 23.2 keV (Cd-Kα1) and 27.5 keV (Te-Kα1) is more probable, with attenuation lengths of 116 and 69 µm, respectively. As shown in our previous works [19,20], 2 mm thick detectors with pixel pitches of 250 µm and an inter-pixel gap of 50 µm showed an increase of the coincidence percentage from 50% to 80% at 22 keV and 60 keV, respectively; this demonstrates as fluorescent X rays, present at 60 keV, give a great contribution to charge sharing. Moreover, fluorescent X rays, escaping from the pixels, can also produce cross-talk events between pixels. Cross-talk events can be given by the collected-charge pulses; i.e., they are created by the charge carriers really collected by the pixels (e.g., fluorescent X rays) or by induced-charge pulses generated on neighboring non-collecting pixels [9,16,18]. These pulses, also called transient pulses, are due to the weighting potential cross-talk [9–11,18,20]; they are characterized by both positive and negative polarities and different shapes [9]. In our investigated energy range (up to 140 keV), a very low number of these transient pulses was detected. This is due to the low investigated photon energies that produce very small transient pulses, which are often below our detection energy threshold (4 keV). Transient pulses are clearly visible at higher energies (e.g., at 662 keV) [9,10]; these pulses measured Sensors 2021, 21, 3669 3 of 13

Sensors 2021, 21, x FOR PEER REVIEW 3 of 13 in temporal coincidence with the collected pulses are strongly used for both spatial and energy resolution improvements in gamma-ray detectors [9,10].

(a) (b)

Figure 1. Evolution of electron cloud size (FWHM) vs. the drift distance in CZT detectors generated by photoelectrons in the energy range of 25–662 keV; Coulomb repulsion and charge diffusion are used in the simulation [26]. (a) Electric field the energy range of 25–662 keV; Coulomb repulsion and charge diffusion are used in the simulation [26]. (a) Electric field of of 5000 V/cm; (b) 10,000 V/cm. 5000 V/cm; (b) 10,000 V/cm. Moreover,The effects fluorescent of charge-sharing X rays, escaping and fluorescence from the cross-talkpixels, can in also the produce measured cross-talk energy eventsspectra between are typically pixels. represented Cross-talk byevents a worsening can be given of the by energy the collected-charge resolution, the pulses presence; i.e., theyof low are energy created tailing by the below charge the carriers photopeaks, really fluorescencecollected by andthe pixels associated (e.g., escapefluorescent peaks, X rays)andan or increaseby induced-charge of the low-energy pulses generated background. on neighboring The state-of-art non-collecting on the pixels mitigation [9,16,18]. of Thesethese effectspulses, is also represented called transient by the simplepulses, are rejection due to of the charge-sharing weighting potential events (CSD:cross-talk charge- [9– 11,18,20];sharing discrimination), they are characterized which is detectedby both positive in temporal and coincidence negative polarities with the and events different of the shapesneighboring [9]. In pixels; our investigated however, the energy high numberrange (up of rejectedto 140 keV), events, a very often low greater number than of 50% these of transientall detected pulses events, was gives detected. a strong This reduction is due to of the throughputlow investigated and the photon counting energies efficiency that produceof the detectors. very small To avoidtransient this, pulses, the rejected which events are often after below CSD canour bedetection recovered energy through thresh- the oldcharge-sharing (4 keV). Transient addition pulses (CSA) are technique, clearly visible which at consistshigher energi of summinges (e.g., theat 662 energies keV) [9,10]; of the thesecoincidence pulses measured events [16 in–18 temporal]. Unfortunately, coincidence as with documented the collected in the pulses literature are strongly [17–21], used the forenergy both recovered spatial and after energy CSA resolution is often lower improvements than true photonin gamma-ray energy, detectors which is [9,10]. due to the presenceThe ofeffects charge of lossescharge-sharing near the region and fluorescence of inter-pixel cross-talk gap. These in losses the measured are related energy to the presence of distorted electric field lines at the inter-pixel gap [14]. In fact, due to the surface spectra are typically represented by a worsening of the energy resolution, the presence of conductivity at the inter-pixel gap, the electric field lines can intersect the surface of the low energy tailing below the photopeaks, fluorescence and associated escape peaks, and inter-pixel gaps, where some charges can be trapped [14,20,23–25]. Generally, the charge an increase of the low-energy background. The state-of-art on the mitigation of these ef- losses depend on the interaction position within the gap, with high effects near the center. fects is represented by the simple rejection of charge-sharing events (CSD: charge-sharing Recently, an interesting technique for charge loss recovery after CSA was proposed by discrimination), which is detected in temporal coincidence with the events of the neigh- our group [20]. This technique, involving double-shared events (m = 2) between adjacent boring pixels; however, the high number of rejected events, often greater than 50% of all pixels, is based on the modeling of the charge losses vs. the interaction position within detected events, gives a strong reduction of the throughput and the counting efficiency of the inter-pixel gap. In particular, we modeled the relation between the summed energy the detectors. To avoid this, the rejected events after CSD can be recovered through the ECSA for two adjacent pixels (m = 2), which are affected by the energy deficit, and the charge-sharing addition (CSA) technique, which consists of summing the energies of the charge-sharing ratio R. As is well known, the charge-sharing ratio R, calculated from coincidencethe ratio between events the [16–18]. energies Unfortunately, of two adjacent as documented pixels R = (pixelin the A literature− pixel B )/([17–21],pixel Athe+ energypixel B), recovered follows the after interaction CSA is often position lower of than the true events photon in the energy, inter-pixel which gap. is due Two to keythe presencefeatures characterize of charge losses this technique:near the region (i) first, of inter-pixel the modeling gap. does These not losses depend are on related the photon to the presenceenergy, but of itdistorted is only relatedelectric to field the lines physical at the and inter-pixel geometrical gap characteristics[14]. In fact, due of to the the electrode surface conductivitylayout; (ii) second, at the itinter-pixel can be easily gap, obtained the electr evenic field with lines uncollimated can intersect photon the surface beams. of This the inter-pixelapproach was gaps, successfully where some applied charges to can several be trapped CZT and [14,20,23–25,]. CdTe pixel detectors Generally, [20 the–25 charge] with lossesimprovements depend on in energythe interaction resolution position and counting within the efficiency. gap, with However, high effects since near this the technique center. is appliedRecently, to shared an interesting events involving technique only for two charge adjacent loss pixels recovery (m = after 2), multiple CSA was coincidences proposed withby ourm group> 2 are [20]. still rejectedThis technique, from the involving measured double-shared energy spectra. events (m = 2) between adjacent pixels, is based on the modeling of the charge losses vs. the interaction position within the inter-pixel gap. In particular, we modeled the relation between the summed energy ECSA for two adjacent pixels (m = 2), which are affected by the energy deficit, and the charge-sharing ratio R. As is well known, the charge-sharing ratio R, calculated from the ratio between the energies of two adjacent pixels R = (pixel A − pixel B)/(pixel A + pixel B),

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follows the interaction position of the events in the inter-pixel gap. Two key features characterize this technique: (i) first, the modeling does not depend on the photon energy, but it is only related to the physical and geometrical characteristics of the electrode layout; (ii) second, it can be easily obtained even with uncollimated photon beams. This approach was successfully applied to several CZT and CdTe pixel detectors [20–25] with improvements in energy resolution and counting efficiency. However, since this technique is ap- Sensors 2021, 21, 3669 4 of 13 plied to shared events involving only two adjacent pixels (m = 2), multiple coincidences with m > 2 are still rejected from the measured energy spectra. TheThe goal goal of of this this work work is is to to propose propose new new approaches approaches for for the the correction correction of the of energythe energy of multipleof multiple coincidence coincidence events. events.

3.3. Detectors Detectors and and Electronics Electronics Charge-sharingCharge-sharing investigations investigations were were performed performed on on several several CZT CZT pixel pixel detectors. detectors. We We usedused CZT CZT detectors detectors characterized characterized by by the the same same anode anode layout layout but but with with different different CZT CZT crystals crys- andtalsthicknesses. and thicknesses. The anodeThe anode layout layout is characterized is characterized by fourby four arrays arrays of 3of× 3 3× pixels3 pixels with with pixelpixel pitches pitches of of 500 500 and and 250 250µ mμm (inter-pixel (inter-pixel gap gap of of 50 50µ m),μm), while while the the cathode cathode is is a a planar planar electrodeelectrode (Figure (Figure2). 2). Different Different CZT CZT crystals crystals were were used. used. Some Some detectors detectors are are based based on on the the travelingtraveling heater heater method method (THM) (THM) [19 [19–21]–21] and and boron boron oxide oxide encapsulated encapsulated vertical vertical Bridgman Bridgman (B- VB)(B-VB) [23,27 [23,27,29],29] CZT CZT crystals. crystals. In addition In addition to the to standardthe standard or low or fluxlow flux LF-THM LF-THM CZT CZT crystals, crys- wetals, also we tested also tested high-flux high-flux HF-THM HF-THM CZT CZT crystals crystals [20 ,[20,30],30], which which were were recently recently produced produced byby Redlen Redlen Technologies Technologies and and characterized characterized by by enhanced enhanced hole hole charge charge transport transport properties properties toto minimize minimize radiation-induced radiation-induced polarization polarization at at high high fluxes. fluxes. The The detectors detectors were were flip-chip flip-chip bondedbonded directly directly to to analog analog charge-sensitive charge-sensitive preamplifiers preamplifiers (CSPs) (CSPs) and and processed processed by by using using digitaldigital pulse pulse processing processing electronics electronics [ 17[17,19].,19]. The The analog analog CSPs CSPs were were based based on on a a fast- fast- and and low-noiselow-noise application application specific specific integrated integrated circuit circuit (PIXIE (PIXIE ASIC) ASIC) developed developed at at RAL RAL (Didcot, (Didcot, UK)UK) [ 31[31].]. The The output output waveforms waveforms from from the the CSPs CSPs are are digitized digitized and and processed processed on-line on-line by by a a 16-channel16-channel digital digital electronics, electronics, which which were were developed developed at at DiFC DiFC of of University University of of Palermo Palermo (Italy)(Italy) [ 17[17,19].,19]. The The digital digital electronics electronics is is based based on on commercial commercial digitizers digitizers (DT5724, (DT5724, 16-bit, 16-bit, 100100 MS/s, MS/s, CAENCAEN SpA, SpA, Italy; Italy; http://www.caen.it http://www.caen.it),, accessedwhere an on original 24 May firmware 2021), where was anup- 109 241 57 originalloaded firmware[32]. Uncollimated was uploaded radiation [32]. Uncollimatedsources (109Cd, radiation 241Am, 57 sourcesCo) and ( collimatedCd, Am, synchro-Co) andtron collimated X-rays (25 synchrotron and 40 keV) X-rays were used (25 and for 40the keV)measurements. were used In for particular, the measurements. collimated Inmicro-beams particular, collimatedwere also used micro-beams at the B16 were test beamline also used at at the the Diamond B16 test Light beamline Source at thesyn- DiamondchrotronLight (Didcot, Source U.K.; synchrotron http://www.d (Didcot,iamond.ac.uk/Beamlin U.K.; http://www.diamond.ac.uk/Beamlines/es/Materials/B16). All detec- Materials/B16tors showed the, accessed effects onof charge 24 May losses 2021). after All detectorsCSA, which showed were successfully the effects of recovered charge losses after after CSA, which were successfully recovered after the application of the new techniques the application of the new techniques presented in the next sections. To simplify the presented in the next sections. To simplify the presentation, we preferred to show the presentation, we preferred to show the results of charge-sharing investigations for only results of charge-sharing investigations for only one detector (2 mm thick HF-THM CZT one detector (2 mm thick HF-THM CZT detector) and some correction results even for the detector) and some correction results even for the others. Generally, the detectors are others. Generally, the detectors are characterized by room-temperature energy resolution characterized by room-temperature energy resolution less than 2 keV at 60 keV. less than 2 keV at 60 keV.

Figure 2. Anode layout of the investigated CZT pixel detectors. Each detector is characterized by Figure 2. Anode layout of the investigated CZT pixel detectors. Each detector is characterized by four arrays of 3 × 3 pixels with pixel pitches of 500 and 250 μm. four arrays of 3 × 3 pixels with pixel pitches of 500 and 250 µm.

4. Multiple Coincidence Measurements and Corrections In this section, we will present the results from time coincidence measurements and the effects of charge-sharing and ﬂuorescence cross-talk in the energy spectra. Special attention will be given to the multiplicity m of coincidence events and the related energy recovery techniques. The coincidence measurements are always referred to the coincidence events of the central pixel with the eight neighboring pixels. We will start with the presentation of the energy spectra typically showed after charge-sharing investigations. In particular, Figure3 presents three different energy spectra of uncollimated 59.5 keV photons from 241Am source, which are related to the central pixel of the 250 µm array of the 2 mm Sensors 2021, 21, x FOR PEER REVIEW 5 of 13

4. Multiple Coincidence Measurements and Corrections In this section, we will present the results from time coincidence measurements and the effects of charge-sharing and fluorescence cross-talk in the energy spectra. Special attention will be given to the multiplicity m of coincidence events and the related energy recovery techniques. The coincidence measurements are always referred to the coincidence events of the central pixel with the eight neighboring pixels. We will start with the Sensors 2021, 21, 3669 presentation of the energy spectra typically showed after charge-sharing investigations.5 of 13 In particular, Figure 3 presents three different energy spectra of uncollimated 59.5 keV photons from 241Am source, which are related to the central pixel of the 250 μm array of thickthe 2 CZTmm thick detector. CZT detector. The black The line black represents line repr theesents energy the energy spectrum spectrum of all events of all events (raw spectrum),(raw spectrum), and the and red the line red is theline spectrum is the spectr of theum events of the in events temporal in temporal coincidence coincidence with all eightwith neighboringall eight neighboring pixels. pixels.

FigureFigure 3.3.Charge-sharing Charge-sharing measurements measurements for fo ther the central central pixel pixel of of the the 250 250µm μm array. array. The The blue blue line line repre- 241 sentsrepresents the uncollimated the uncollimated241Am spectrumAm spectrum after charge-sharing after charge-sharing discrimination discrimination (CSD). The(CSD). raw The spectrum raw spectrum (black line) of all events and the spectrum of the coincidence events with all eight neigh- (black line) of all events and the spectrum of the coincidence events with all eight neighboring pixels boring pixels (red line) are also shown. The yellow inset shows the layout of the anode of the de- (red line) are also shown. The yellow inset shows the layout of the anode of the detector. tector. The percentage of coincidence events is very high (79%), and the typical distortions The percentage of coincidence events is very high (79%), and the typical distortions related to charge-sharing and fluorescent cross-talk are clearly visible: the fluorescent peaks related to charge-sharing and fluorescent cross-talk are clearly visible: the fluorescent at 23.2 and 27.5 keV, the escape peaks at 36.3 and 32 keV, the low-energy background andpeaks tailing. at 23.2 The and blue 27.5 line keV, is the the spectrum escape peaks after charge-sharingat 36.3 and 32 keV, discrimination the low-energy (CSD), back- i.e., afterground the rejectionand tailing. of coincidenceThe blue line events is the (79%). spectrum The coincidence after charge-sharing analysis was discrimination performed with(CSD), acoincidence i.e., after the time rejection window of coincidenc (CTW) ofe 200 events ns, ensuring(79%). The the co detectionincidenceof analysis all events; was typically,performed about with 90% a coincidence of coincidence time events window are (CTW) detected of in200 a ns, CTW ensuring of 30 ns. the The detection CSD works of all well,events; allowing typically, the about rejection 90% of of all coincidence charge-sharing events distortions, are detected even in if a it CTW produces of 30 a ns. strong The reductionCSD works of thewell, pixel allowing throughput the rejection and counting of all efficiencycharge-sharing (79% rejected distortions, events). even The if tailingit pro- belowduces thea strong main photopeakreduction of is the not pixel mitigated; throughp theseut events and counting are not in efficiency temporal (79% coincidence rejected withevents). neighboring The tailing pixels below due the to theirmain energies photopeak being is not below mitigated; the detection these energyevents thresholdare not in (4temporal keV). Moreover, coincidence escape with peaks neighboring are also pixels present due in to the their spectra energies even being after below CSD duethe de- to fluorescencetection energy events threshold escaping (4 keV). from Moreover, the cathode es orcape absorbed peaks onare the also guard-ring. present in the spectra evenThe after multiplicity CSD due tom fluorescenceof the coincidence events events,escaping i.e., from the numberthe cathode of the or involvedabsorbed pixelson the withinguard-ring. a coincidence detection, was also measured (Figure4). We estimated the multiplicity of theThe events multiplicity of the central m of pixel the coincidence (pixel no. 5) forevents, both i.e., arrays theand number at different of the energies:involved 109pixelsCd (mainwithin energy a coincidence line at 22.1 detection, keV), 241 wasAm also (main meas energyured line (Figure at 59.5 4). keV), We es andtimated57Co (mainthe multiplic- energy lineity of at the 122.1 events keV). of Generally, the central the pixel presence (pixel of no coincidence. 5) for both events arrays with andm at > different2 is increased energies: for energies109Cd (main (241 Amenergy and line57Co at sources)22.1 keV), greater 241Am than (main the energy K-shell line absorption at 59.5 keV), energy and of 57Co the (main CZT material, due to the fluorescence X-ray events.

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energy line at 122.1 keV). Generally, the presence of coincidence events with m > 2 is in- Sensors 2021, 21, 3669 creased for energies (241Am and 57Co sources) greater than the K-shell absorption energy6 of 13 of the CZT material, due to the fluorescence X-ray events.

FigureFigure 4.4. The multiplicity m of the coincidence events events of of the the central central pixels pixels for for the the 250 250 and and 500 500 μµmm arrays.arrays. TheThe multiplicitymultiplicity mm isis referredreferred toto thethe numbernumber ofof pixelspixels involvedinvolved inin aa coincidencecoincidence detection.detection.

TheThe analysisanalysis ofof multiplicitymultiplicity waswas alsoalso performedperformed onon aa sub-pixelsub-pixel levellevel withwith collimatedcollimated synchrotronsynchrotron X-rayX-ray beams. beams. We We measured measured the the multiplicity multiplicity of the of coincidencethe coincidence events events between be- twotween adjacent two adjacent pixels at pixels different at different beam positions. beam po Insitions. particular, In particular, microscale microscale line scans line between scans thebetween centers the of centers the adjacent of the pixelsadjacent were pixels performed were performed with collimated with collimated (10 µm × 10(10µ μm)m syn-× 10 chrotronμm) synchrotron X-ray beams X-ray at energiesbeams at below energies (25 below keV) and (25 above keV) and (40 keV) above the (40 K-shell keV) absorptionthe K-shell energyabsorption of the energy CZT material.of the CZT During material. the line During scanning the line between scanning the twobetween pixels, the we two acquired, pixels, atwe each acquired, beam positionat each beam (position position steps (position of 25 µm), steps the of data 25 fromμm), allthe nine data pixels from all of thenine investi- pixels gatedof the array.investigated Figure5 array.shows Figure an overview 5 shows of thean overview multiplicity of them vs. multiplicity the beam position m vs. the for beam two differentposition for line two scans. different The line line scanning scans. The near line the scanning central near region the of central both pixelsregion(Figure of both5 a,c)pix- highlightsels (Figure the 5a,c) presence highlights of coincidence the presence events of co mainlyincidence near events the inter-pixel mainly near gap, the with inter-pixel a spatial µ extensiongap, with beyonda spatial the extension gap (50 beyondm) at 40 the keV, gap due (50 toμm) fluorescence at 40 keV, events;due to fluorescence double coincidence events; m eventsdouble ( coincidence= 2) represent events the ( dominantm = 2) represent contribution the dominant to the overall contribution coincidence to the events. overall Near co- the edge region of the pixels (Figure5b,d), double coincidence events are present over all incidence events. Near the edge region of the pixels (Figure 5b,d), double coincidence the pixel area; the number of multiple coincidence events (m > 2) is strongly increased events are present over all the pixel area; the number of multiple coincidence events (m > near the inter-pixel gap, which is due to both charge-sharing and fluorescence cross-talk. 2) is strongly increased near the inter-pixel gap, which is due to both charge-sharing and In the following, we will investigate the features of the various multiplicities, presenting fluorescence cross-talk. In the following, we will investigate the features of the various dedicated correction techniques. multiplicities, presenting dedicated correction techniques. 4.1. Coincidence Events with Multiplicity m = 2 4.1. Coincidence Events with Multiplicity m = 2 The predominant contribution to the overall coincidence events is represented by the eventsThe with predominant multiplicity contributionm = 2, as clearly to the shownoverall incoincidence Figure4. Double events is coincidence represented events by the areevents mainly with due multiplicity to charge-shared m = 2, as eventsclearly near shown the in inter-pixel Figure 4. gap,Double fluorescent coincidence cross-talk, events andare mainly mixed shared/fluorescentdue to charge-shared events. events Pictures near ofthe typical inter-pixel fluorescent gap, fluorescent cross-talk and cross-talk, charge sharedand mixed events shared/fluorescent are shown in Figure events.6a,b. Pictures To better of typical highlight fluorescent the different cross-talk effects and ofcharge the twoshared main events contributes, are shown we in analyzed Figure 6a,b. the doubleTo better coincidences highlight the of different two adjacent effects pixels of the for two a collimatedmain contributes, irradiation we analyzed (10 × 10 theµm 2double) with synchrotroncoincidences Xof rays two atadjacent the center pixels of onefor a of colli- the twomated pixels irradiation (Figure 6(10). Here,× 10 μ them2) energywith synchrotron spectra of theX rays central at the pixel center (Figure of one6c) of and the the two adjacentpixels (Figure pixel 6). (Figure Here,6 d)the are energy shown. spectra All events of the ofcentral the adjacent pixel (Figure pixel 6c) (green and pixelthe adjacent no. 4) are in double temporal coincidence with events of the central pixel (black pixel no. 5); the shared events and fluorescent events are clearly visible, and the results after charge-sharing addition (CSA) are presented in Figure7. The effects of charge-sharing and fluorescent cross-talk events after CSA are well distinguished. The energy of fluorescent cross events is fully recovered after CSA, as shown by the energy peak and the two kinks at R = 0.160 Sensors 2021, 21, x FOR PEER REVIEW 7 of 13

pixel (Figure 6d) are shown. All events of the adjacent pixel (green pixel no. 4) are in double temporal coincidence with events of the central pixel (black pixel no. 5); the shared events and fluorescent events are clearly visible, and the results after charge-sharing addition (CSA) are presented in Figure 7. The effects of charge-sharing and fluorescent cross- Sensors 2021, 21, 3669 7 of 13 talk events after CSA are well distinguished. The energy of fluorescent cross events is fully recovered after CSA, as shown by the energy peak and the two kinks at R = 0.160 and R = 0.375and R related= 0.375 torelated the 23.2 to and the 27.5 23.2 keV and fluoresc 27.5 keVent X-rays, ﬂuorescent respectively; X-rays, respectively;while charge losses while characterizedcharge losses characterizedthe double-shared the double-shared events after CSA, events which after are CSA, highlighted which are by highlighted a reduction by ofa reductionthe centroid of theof the centroid main peak. of the main peak.

Figure 5. Results of microscale line scanning with synchrotron X-rays between the centers of two adjacent pixels; (a,b) at energy below (25 keV) and (c,d) above (40 keV)keV) thethe K-shellK-shell absorptionabsorption energyenergy of the CZT material.material. The multiplicity m at various beam positions was measured: (a,,c) near thethe centralcentral regionregion ofof bothboth pixels,pixels, ((bb,,dd)) nearnear thethe edgeedge region.region.

To recover the energy of double coincidences, we proposed two separate procedures forfor adjacent andand diagonaldiagonal pixels. pixels. The The double double coincidence coincidence events events between between adjacent adjacent pixels pixels are aremainly mainly dominated dominated by charge-shared by charge-shared events events and byand a smallby a small contribute contribute of ﬂuorescent of fluorescent cross- cross-talktalk events. events. The energy The energy of double of double shared shared events events can be can recovered be recovered through through the correction the cor- rectiontechnique, technique, termed termeddouble charge-sharing double charge-sharing correction correction(double CSC (double), as CSC presented), as presented in our previous in our previouswork [20 ].work [20].

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Figure 6. MeasurementsMeasurements of of fluorescence ﬂuorescence cross-talk cross-talk ( (aa)) and and charge-sharing ( (b)) events. Energy Energy spectra spectra at at 40 40 keV keV of of two Figure 6. Measurements of fluorescence cross-talk (a) and charge-sharing (b) events. Energy spectra at 402 keV of two adjacent pixels: ( c) pixel no. 5 and ( d) pixel no. 4. We used aa collimatedcollimated X-rayX-ray synchrotronsynchrotron beambeam (10(10× × 10 μµm2)) interacting interacting adjacent pixels: (c) pixel no. 5 and (d) pixel no. 4. We used a collimated X-ray synchrotron beam (10 × 10 μm2) interacting at the center of the central pixel (black pixel no.5). All even eventsts of the adjacent pixel (green pixel no. 4) 4) are in temporal at the center of the central pixel (black pixel no.5). All events of the adjacent pixel (green pixel no. 4) are in temporal coincidence with the central pixel with multiplicity m = 2. coincidence with the central pixel with multiplicity m = 2.

(a) (b) (a) (b) Figure 7. Experimental results after CSA for m = 2 coincidence events between adjacent pixels. (a) The 2D scatter plot of Figure 7. Experimental resultsresults afterafter CSACSA for form m= = 2 2 coincidence coincidence events events between between adjacent adjacent pixels. pixels. (a )( Thea) The 2D 2D scatter scatter plot plot of the of the energy ECSA after CSA versus the charge-sharing ratio R. (b) The energy spectrum after CSA. theenergy energyECSA ECSAafter after CSA CSA versus versus the the charge-sharing charge-sharing ratio ratioR.( Rb.) ( Theb) The energy energy spectrum spectrum after after CSA. CSA.

It consists of the modeling of the 2D distribution of the energy after CSA (ECSA) vs. ItIt consists ofof thethe modelingmodeling of of the the 2D 2D distribution distribution of theof the energy energy after after CSA CSA (ECSA (E)CSA vs.) thevs. the charge-sharing ratio R, as shown in Figure 8a for uncollimated109 109Cd source. This tech- thecharge-sharing charge-sharing ratio ratioR, as R shown, as shown in Figure in Figure8a for 8a uncollimated for uncollimatedCd 109 source.Cd source. This This technique technique allows the energy reconstruction of double shared events from uncollimated and niqueallows allows the energy the energy reconstruction reconstruction of double of do shareduble shared events events from uncollimatedfrom uncollimated and poly- and poly-energetic sources [20]. Figure 8b presents the results after the application of standard poly-energeticenergetic sources sources [20]. Figure[20]. Figure8b presents 8b presents the results the results after theafter application the application of standard of standard CSA CSA and double CSC. After double CSC, the energy loss is recovered, and the energy CSAand doubleand double CSC. AfterCSC. doubleAfter double CSC, the CSC, energy the lossenergy is recovered, loss is recovered, and the energy and the resolution energy resolution is also improved. At energies greater than the K-shell absorption energy of the resolutionis also improved. is also improved. At energies At energies greater grea thanter the than K-shell the K-shell absorption absorption energy energy of the of CZT the

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CZTmaterial, material, the double the double coincidence coincidence events events between between adjacent adjacent pixels pixels also also contain contain ﬂuorescent fluores- centcross-talk cross-talk events, events, which which can be can easily be correctedeasily corrected after standard after standard CSA (Figure CSA7 ).(FigureThe selection 7). The selectionof these eventsof these (ﬂuorescent events (fluorescent event and event escape and peak escape event) peak is event) simple is for simple mono-energetic for mono- energeticX-ray sources, X-ray but sources, it is challenging but it is challenging for poly-energetic for poly-energetic sources. The sources. dedicated The selection dedicated of selectionthese events, of these based events, on stripping based on procedures stripping with procedures simulated with response simulated functions response [33 ],func- will tionsbe investigated [33], will be further investigated in the future. further in the future.

(a) (b)

Figure 8. ((aa)) Two-dimensional Two-dimensional (2D) (2D) scatter scatter plot plot of of th thee summed summed energy energy of ofthe the coincidence coincidence events events (m (=m 2)= between 2) between pixel pixel no. 109 5no. and 5 andpixel pixel no. 8, no. after 8, afterCSA, CSA,versus versus the ratio the R ratio (uncollimatedR (uncollimated 109Cd source).109Cd source). The red Theline is red the line modeling is the modeling function, function,a parabola a with vertex at the point (0, ECSA (0)) [20], used to correct charge losses. (b) The energy spectra after CSA (black line) and parabola with vertex at the point (0, ECSA (0)) [20], used to correct charge losses. (b) The energy spectra after CSA (black after double CSC (red line). The complete recovery of the energy after double CSC and improvements of the energy reso- line)after double and after CSC double (red line). CSC (redThe complete line). The recovery complete of recoverythe energy of after the energy double after CSC doubleand improvements CSC and improvements of the energy of reso- the lution are clearly visible. energy resolution are clearly visible. Concerning the double coincidence events between diagonal pixels, we observed that Concerning the double coincidence events be betweentween diagonal pixels, we observed that they are due to pure fluorescence cross-talk events. This is clearly shown in Figure 9. In theythey are are due to pure fluorescencefluorescence cross-talk ev events.ents. This This is is clearly shown shown in in Figure 99.. In particular, thethe 2D2D scatter scatter plot plot of of Figure Figure9a highlights9a highlights the the energy energy recovery recovery of the of energy the energy after afterstandard standard CSA atCSA about at aboutR = ± 0.22R = ±0.22 and R and= ± R0.076, = ±0.076, which which are related are related to the to fluorescent the fluorescent X rays 241 Xof rays 23.2 of and 23.2 27.5 and keV, 27.5 respectively keV, respectively (241Am source).(241Am source). The same The result same is result also confirmed is also confirmed through throughthe energy the spectrum energy spectrum after CSA after (Figure CSA9b). (Figure At energies 9b). At below energies the K-shellbelow the absorption K-shell absorp- energy 109 tionof CZT energy (e.g., of by CZT using (e.g.,109Cd by source), using109 noCd double source), coincidence no double events coincidence were observed events were between ob- serveddiagonal between pixels. diagonal pixels.

(a) (b) Figure 9. (a) Two-dimensional (2D) scatter plot of the summed energy of the coincidence events (m = 2) between diagonal Figure 9. (a(a) )Two-dimensional Two-dimensional (2D) (2D) scatter scatter plot plot of ofthe the summed summed energy energy of the of coincidence the coincidence events events (m = 2) (m between= 2) between diagonal di- pixels (no. 5 and pixel no. 9), after CSA, versus the ratio R. (b) The energy spectrum shows the absence of charge losses agonal pixels (no. 5 and pixel no. 9), after CSA, versus the ratio R.(b) The energy spectrum shows the absence of after CSA, demonstrating that the double coincidence events between diagonal pixels are mainly due to the fluorescent/es- charge losses after CSA, demonstrating that the double coincidence events between diagonal pixels are mainly due to the cape events. ﬂuorescent/escape events.

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4.2.4.2. Coincidence Coincidence Events Events with with Multiplicity Multiplicity m m > > 2 2 TheThe results results of of Figure Figure 44 pointpoint out out the the presen presencece of of coincidence coincidence events events with with multiplicity multiplic- mity >m 2,> especially 2, especially forfor the the 250 250 μmµm array. array. These These events events are are created created by by mixed mixed fluores- ﬂuores- cent/sharedcent/shared coincidence coincidence eventsevents atat the the inter-pixel inter-pixel gap. gap. In In particular, particular, some some triple triple coincidence coinci- denceevents events (i.e., m (i.e.,= 3) m can = 3) be can often be often obtained obtained from from a true a true quadruple quadruple coincidence, coincidence, where where the theenergy energy of theof the pulse pulse of oneof one pixel pixel is belowis below the th detectione detection energy energy threshold, threshold, e.g., e.g., of of 4 keV4 keV in inour our case. case. The The recovery recovery of of the the energy energy of of multiple multiple coincidence coincidence eventsevents isis stillstill challenging. In FigureFigure 10,10, we we present present the the energy energy spectra spectra of of co coincidenceincidence events events after after CSA CSA at at different different multi- multi- plicitiesplicities and and energies. energies. All All ener energygy spectra spectra suffer suffer from from charge charge losses losses after after CSA. CSA. However, However, the linearthe linear behavior behavior of the of summed the summed energy energy ECSA withECSA thewith true the photon true photon energy energy(Figure (Figure10d) allows 10d) theallows recovery the recovery of the energy of the through energy througha simple aen simpleergy re-calibration energy re-calibration procedure. procedure. We point out We thatpoint the out 4 keV that intercept the 4 keV of intercept the linear of function the linear for function m = 3 (the for redm = line 3 (the of Figure red line 10d) of Figure highlights 10d) thehighlights possible the measurement possible measurement of triple coincidenc of triplee events coincidence from true events quadruple from true coincidences, quadruple wherecoincidences, the energy where of one the energyof the four of one pixels of the is fourbelow pixels the detection is below thethreshold detection (4 keV), threshold and therefore,(4 keV), and it is therefore, not detected. it is not detected.

(a) (b)

Figure 10. (a) 109Cd, (b) 241241Am, and (c) 5757Co spectra after CSA at various multiplicities. (d) The linearity of ECSA with the Figure 10. (a) Cd, (b) Am, and (c) Co spectra after CSA at various multiplicities. (d) The linearity of ECSA with the truetrue photon photon energy energy opens up to a correction of charge losses after CSA through aa simplesimple energyenergy re-calibration.re-calibration.

Therefore,Therefore, we we applied applied the the va variousrious proposed proposed correction techniques techniques for for each related multiplicity.multiplicity. In particular, we applied, for the central pixel of 500/250 μµmm arrays, arrays, the the doubledouble CSCCSC techniquetechnique on on m == 2 2 events events between between adjacent adjacent pixels, pixels, the standardstandard CSA for m = 2 2 events events betweenbetween diagonal diagonal pixels, pixels, and and the the re-calibratedre-calibrated CSA CSA forfor both both m = 3 and m = 4 events. The completecomplete correction correction is is termed termed multiplemultiple CSC CSC technique.technique. The The results results for for two two different different CZT CZT detectorsdetectors are are shown shown in in Figure Figure 11.11.

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(a) (b)

(c) (d) Figure 11. The raw energy spectra (black lines) and the corrected spectra (red lines) after the multiple charge-sharing correc- Figure 11. The raw energy spectra (black lines) and the corrected spectra (red lines) after the multiple charge-sharing tion (CSC) of the central pixel of 500/250 μm arrays for different detectors: (a–c) the high-flux HF-THM CZT detector, (d) correction (CSC) of the central pixel of 500/250 µm arrays for different detectors: (a–c) the high-flux HF-THM CZT detector, the low-flux LF-THM CZT detector. We applied the double CSC technique on m = 2 events between adjacent pixels, the d m (standard) the low-flux CSA for LF-THM m = 2 events CZT between detector. diagonal We applied pixels, the and double the re-calibrated CSC technique CSA on for both= 2 events m = 3 and between m = 4 adjacentevents. The pixels, energy the standardresolution CSA was forslightlym = 2improved. events between diagonal pixels, and the re-calibrated CSA for both m = 3 and m = 4 events. The energy resolution was slightly improved. 5. Conclusions 5. Conclusions Original techniques that are able to correct the charge losses after charge-sharing ad- Original techniques that are able to correct the charge losses after charge-sharing dition (CSA) in CZT pixel detectors were presented. Different approaches were used for addition (CSA) in CZT pixel detectors were presented. Different approaches were used adjacent and diagonal pixels, taking into account the number of involved pixels (i.e., the for adjacent and diagonal pixels, taking into account the number of involved pixels (i.e., multiplicity m). One approach, exploiting the relation between the summed energy after the multiplicity m). One approach, exploiting the relation between the summed energy CSA and the charge-sharing ratio R of double coincidence events (m = 2), allowed the re- after CSA and the charge-sharing ratio R of double coincidence events (m = 2), allowed covery of charge losses between adjacent pixels. A second technique, based on the linear the recovery of charge losses between adjacent pixels. A second technique, based on behavior of charge losses after CSA with the true photon energy, was also implemented the linear behavior of charge losses after CSA with the true photon energy, was also to reconstruct multiple coincidence events with m > 2. The energy of double coincidence implemented to reconstruct multiple coincidence events with m > 2. The energy of double events between diagonal pixels, mainly due to fluorescence cross-talk events, was suc- coincidence events between diagonal pixels, mainly due to fluorescence cross-talk events, cessfullywas successfully recovered recovered after the after standard the standard CSA. CSA. Results on on different CZT pixel detectors sh showedowed improved improved counting counting efficiency efficiency com- com- pared to to using using only only isolated isolated events events (i.e., (i.e., after after CSD) CSD) and andimproved improved energy energy resolution resolution com- paredcompared to the to standard the standard CSA CSA techniques. techniques.

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Author Contributions: Conceptualization, L.A. and A.B.; formal analysis, L.A., A.B., G.G., F.P., G.R., D.C., M.B.; investigation, L.A., A.B., F.P., M.C.V., P.S., A.Z., M.M.; writing—original draft preparation, A.B. and L.A.; writing—review and editing, all authors; supervision, L.A.; project administration, L.A.; funding acquisition, L.A. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Italian Ministry for University and Research (MUR), under AVATAR X project No. POC01_00111, by the Science and Technology Facilities Council (UK), under the Centre for Instrumentation Sensors Managed Programme 2016–2017, and by the Diamond Light Source (proposal MT20545). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Barber, W.C.; Wessel, J.C.; Nygard, E.; Iwanczyk, J.S. Energy dispersive CdTe and CdZnTe detectors for spectral clinical CT and NDT applications. Nucl. Instr. Meth. A 2015, 784, 531–537. [CrossRef][PubMed] 2. Del Sordo, S.; Strazzeri, M.; Agnetta, G.; Biondo, B.; Celi, F.; Giarrusso, S.; Mangano, A.; Russo, F.; Caroli, E.; Donati, A.; et al. Spectroscopic performances of 16 × 16 pixel CZT imaging hard-X-ray detectors. Nuovo Cimento B 2004, 119, 257–270. 3. Iwanczyk, J.; Nygard, E.; Meirav, O.; Arenson, J.; Barber, W.C.; Hartsough, N.E.; Malakhov, N.; Wessel, J.C. Photon Counting Energy Dispersive Detector Arrays for X-ray Imaging. IEEE Trans. Nucl. Sci. 2009, 56, 535–542. [CrossRef][PubMed] 4. Seller, P.; Bell, S.; Cernik, R.J.; Christodoulou, C.; Egan, C.K.; Gaskin, J.A.; Jacques, S.; Pani, S.; Ramsey, B.D.; Reid, C.; et al. Pixellated Cd(Zn)Te high-energy X-ray instrument. J. Inst. 2011, 6, C12009. [CrossRef] 5. Szeles, C.; Soldner, S.A.; Vydrin, S.; Graves, J.; Bale, D.S. CdZnTe Semiconductor Detectors for Spectroscopic X-ray Imaging. IEEE Trans. Nucl. Sci. 2008, 55, 572–582. [CrossRef] 6. Iniewski, K. CZT detector technology for medical imaging. J. Inst. 2014, 9, C11001. [CrossRef] 7. Del Sordo, S.; Abbene, L.; Caroli, E.; Mancini, A.M.; Zappettini, A.; Ubertini, P. Progress in the development of CdTe and CdZnTe semiconductor radiation detectors for astrophysical and medical applications. Sensors 2009, 9, 3491–3526. [CrossRef] 8. Sammartini, M.; Gandola, M.; Mele, F.; Garavelli, B.; Macera, D.; Pozzi, P.; Bertuccio, G. A CdTe pixel detector–CMOS preamplifier for room temperature high sensitivity and energy resolution X and γ ray spectroscopic imaging. Nucl. Instr. Meth. A 2018, 910, 168–173. [CrossRef] 9. Abbene, L.; Gerardi, G.; Principato, F.; Bettelli, M.; Seller, P.; Veale, M.C.; Fox, O.; Sawhney, K.; Zambelli, N.; Benassi, G.; et al. Recent advances in the development of high-resolution 3D cadmium–zinc–telluride drift strip detectors. J. Synchrotron Rad. 2020, 27, 1564–1576. [CrossRef] 10. Bolotnikov, A.E.; Camarda, G.S.; De Geronimo, G.; Fried, J.; Hodges, D.; Hossain, A.; James, R.B. A 4 × 4 array module of position-sensitive virtual Frisch-grid CdZnTe detectors for gamma-ray imaging spectrometers. Nucl. Instr. Meth. A 2020, 954, 161036. [CrossRef] 11. Howalt Owe, S.; Kuvvetli, I.; Budtz-Jørgensen, C.; Zoglauer, A. Evaluation of a Compton camera concept using the 3D CdZnTe drift strip detectors. J. Inst. 2019, 14, C01020. 12. Zhang, F.; Herman, C.; He, Z.; De Geronimo, G.; Vernon, E.; Fried, J. Characterization of the H3D ASIC Readout System and 6.0 cm 3-D Position Sensitive CdZnTe Detectors. IEEE Trans. Nucl. Sci. 2012, 59, 236–242. [CrossRef] 13. Ariño-Estrada, G.; Mitchell, G.S.; Kim, H.; Du, J.; Kwon, S.I.; Cirignano, L.J.; Shah, K.S.; Cherry, S.R. First Cerenkov charge- induction (CCI) TlBr detector for TOF-PET and proton range verification. Phys. Med. Biol. 2019, 64, 175001. [CrossRef] 14. Bolotnikov, A.E.; Camarda, G.C.; Wright, G.W.; James, R.B. Factors Limiting the Performance of CdZnTe Detectors. IEEE Trans. Nucl. Sci. 2005, 52, 589–598. [CrossRef] 15. Guerra, P.; Santos, A.; Darambara, D. Development of a simplified simulation model for performance characterization of a pixellated CdZnTe multimodality imaging system. Phys. Med. Biol. 2008, 52, 589–598. [CrossRef] 16. Koenig, T.; Hamann, E.; Procz, S.; Ballabriga, R.; Cecilia, A.; Zuber, M.; Fiederle, M. Charge Summing in Spectroscopic X-Ray Detectors With High-Z Sensors. IEEE Trans. Nucl. Sci. 2013, 60, 4713–4718. [CrossRef] 17. Abbene, L.; Gerardi, G.; Principato, F. Digital performance improvements of a CdTe pixel detector for high flux energy-resolved X-ray imaging. Nucl. Instr. Meth. A 2015, 777, 54–62. [CrossRef] 18. Kim, J.K.; Anderson, S.E.; Kaye, W.; Zhang, F.; Zhu, Y.; Kaye, S.J.; He, Z. Charge sharing in common-grid pixelated CdZnTe detectors. Nucl. Instr. Meth. A 2011, 654, 233–243. [CrossRef] 19. Abbene, L.; Principato, F.; Gerardi, G.; Bettelli, M.; Seller, P.; Veale, M.C.; Zappettini, A. Digital fast pulse shape and height analysis on cadmium–zinc–telluride arrays for high-flux energy-resolved X-ray imaging. J. Synchrotron Rad. 2018, 25, 257–271. [CrossRef] 20. Abbene, L.; Gerardi, G.; Principato, F.; Bettelli, M.; Seller, P.; Veale, M.C.; Zappettini, A. Dual-polarity pulse processing and analysis for charge-loss correction in cadmium–zinc–telluride pixel detectors. J. Synchrotron Rad. 2018, 25, 1078–1092. [CrossRef] Sensors 2021, 21, 3669 13 of 13

21. Buttacavoli, A.; Principato, F.; Gerardi, G.; Bettelli, M.; Sarzi Amadè, N.; Zappettini, A.; Abbene, L. Room-temperature performance of 3 mm-thick cadmium zinc telluride pixel detectors with sub-millimetre pixelization. J. Synchrotron Rad. 2020, 27, 1180–1189. [CrossRef] 22. Lai, X.; Shirono, J.; Araki, H.; Budden, B.; Cai, L.; Kawata, G.; Thompson, R. Modeling Photon Counting Detector Anode Street Impact on Detector Energy Response. IEEE Trans. Rad. Plas. Med. Sci. 2020.[CrossRef] 23. Abbene, L.; Principato, F.; Gerardi, G.; Buttacavoli, A.; Cascio, D.; Bettelli, M.; Zappettini, A. Room-Temperature X-ray response of cadmium-zinc-Telluride pixel detectors grown by the vertical Bridgman technique. J. Synchrotron Rad. 2020, 27, 319–328. [CrossRef] 24. Bugby, S.L.; Koch-Mehrin, K.A.L.; Veale, M.C.; Wilson, M.D.; Lees, J.E. Energy-loss correction in charge sharing events for improved performance of pixellated compound semiconductors. Nucl. Instr. Meth. A 2019, 940, 142–151. [CrossRef] 25. Koch-Mehrin, K.A.L.; Lees, J.E.; Bugby, S.L. A spectroscopic Monte-Carlo model to simulate the response of pixelated CdTe based detectors. Nucl. Instr. Meth. A 2020, 976, 164241. [CrossRef] 26. Bettelli, M.; Amadè, N.S.; Calestani, D.; Garavelli, B.; Pozzi, P.; Macera, D.; Zappettini, A. A ﬁrst principle method to simulate the spectral response of CdZnTe-based X- and gamma-ray detectors. Nucl. Instr. Meth. A 2020, 960, 163663. [CrossRef] 27. Abbene, L.; Gerardi, G.; Turturici, A.A.; Raso, G.; Benassi, G.; Bettelli, M.; Principato, F. X-ray response of CdZnTe detectors grown by the vertical Bridgman technique: Energy, temperature and high ﬂux effects. Nucl. Instr. Meth. A 2016, 835, 1–12. [CrossRef] 28. Ballabriga, R.; Alozy, J.; Bandi, F.N.; Campbell, M.; Egidos, N.; Fernandez-Tenllado, J.M.; Tlustos, L. Photon Counting Detectors for X-ray Imaging with Emphasis on CT. IEEE Trans. Rad. Plas. Med. Sci. 2020.[CrossRef] 29. Auricchio, N.; Marchini, L.; Caroli, E.; Zappettini, A.; Abbene, L.; Honkimaki, V. Charge transport properties in CdZnTe detectors grown by the vertical Bridgman technique. J. Appl. Phys. 2011, 110, 124502. [CrossRef] 30. Veale, M.C.; Booker, P.; Cross, S.; Hart, M.D.; Jowitt, L.; Lipp, J.; Prekas, G. Characterization of the Uniformity of High-Flux CdZnTe Material. Sensors 2020, 20, 2747. [CrossRef] 31. Veale, M.C.; Bell, S.J.; Jones, L.L.; Seller, P.; Wilson, M.D.; Allwork, C.; Cernik, R.C. An ASIC for the Study of Charge Sharing Effects in Small Pixel CdZnTe X-Ray Detectors. IEEE Trans. Nucl. Sci. 2011, 58, 2357–2362. [CrossRef] 32. Gerardi, G.; Abbene, L. A digital approach for real time high-rate high-resolution radiation measurements. Nucl. Instr. Meth. A 2014, 768, 46–54. [CrossRef] 33. Mihajima, S.; Imagawa, K.; Matsumoto, M. CdZnTe detector in diagnostic x-ray spectroscopy. Med. Phys. 2002, 29, 1421–1429. [CrossRef][PubMed]