Cadmium Zinc Telluride Detectors for a Next-Generation Hard X-ray Telescope
©© // creativecommons.org / licenses / by-nc-nd / / Cadmium Zinc Telluride Detectors for a Next-Generation Hard X-ray Telescope
J. Tang a, ∗ , F. Kislat b , H. Krawczynski a a Washington University in St. Louis, Physics Department, 1 Brookings Dr., CB 1105, St. Louis, MO 63130 b University of New Hampshire, Department of Physics & Astronomy and Space Science Center, 8 College Rd, Durham, NH 03824
Abstract
We are currently developing Cadmium Zinc Telluride (CZT) detectors for a next-generation space-borne hard X-ray telescope whichcan follow up on the highly successful
NuSTAR (Nuclear Spectroscopic Telescope Array) mission. Since the launch of
NuSTAR in2012, there have been major advances in the area of X-ray mirrors, and state-of-the-art X-ray mirrors can improve on
NuSTAR’s angular resolution of ∼ (cid:48)(cid:48) or even 5 (cid:48)(cid:48) HPD. Consequently, the size of the detector pixelsmust be reduced to match this resolution. This paper presents detailed simulations of relatively thin (1 mm thick) CZT detectorswith hexagonal pixels at a next-neighbor distance of 150 µ m. The simulations account for the non-negligible spatial extent of thedeposition of the energy of the incident photon, and include detailed modeling of the spreading of the free charge carriers as theymove toward the detector electrodes. We discuss methods to reconstruct the energies of the incident photons, and the locationswhere the photons hit the detector. We show that the charge recorded in the brightest pixel and six adjacent pixels su ffi ces to obtainexcellent energy and spatial resolutions. The simulation results are being used to guide the design of a hybrid application-specificintegrated circuit (ASIC)-CZT detector package. Keywords:
High energy X-ray astrophysics, Instrumentation, Solid state detectors, CZT, Detectors
1. Introduction
Cadmium Zinc Telluride (CZT) detectors are an attractivedetector technology for hard X-ray astronomy as they o ff er ex-cellent spatial resolutions, good energy resolutions, and, com-pared to Si and Ge detectors, much larger photoelectric e ff ectcross sections at hard X-ray energies. A CZT imager may beused on a next-generation telescope succeeding the space-basedhard X-ray telescope NuSTAR (Harrison et al., 2013). The highstoppping power and excellent energy resolution of the
NuS-TAR
CZT detectors enabled it to image the Cassiopeia A (CasA) supernova remnant in the 67 . . Ti (Grefenstette et al., 2014;Boggs et al., 2015; Grefenstette et al., 2017). Contrary to thesoft X-ray lines detected previously, the nuclear Ti emissiondirectly tracks the yield of nuclear material independent of thetemperature and density of the ejecta (Grefenstette et al., 2014;Boggs et al., 2015; Grefenstette et al., 2017).The recently developed monocrystalline silicon X-ray mir-rors (Zhang et al., 2018) or electro-formed-nickel replicated(ENR) X-ray optics (Gaskin et al., 2015) promise angular reso-lutions with Half Power Diameters (HPD) of between a few arc-seconds and 15 arcseconds – even at hard X-ray energies. Theproposed
HEX-P (Madsen et al., 2018) and
BEST (Krawczynskiet al., 2012) observatories seek to capitalize on this technology,as the point source sensitivity scales linearly with the angularresolution. Nyquist sampling the images provided by the im-proved X-ray mirrors requires detectors with excellent spatial ∗ Corresponding author resolutions. Our group is thus leading the development of newsmall-pixel CZT detectors with center-to-center pitch of 150microns and hexagonal pixels, improving by a factor of fourover
NuSTAR’s
CZT detectors (605-micron pixel pitch).This paper discusses the simulations performed for the de-sign of the third-generation Hyperspectral Energy-resolving X-ray Imaging Detector (HEXID3 Li et al., 2017, 2018), whichfeatures hexagonal pixels at a next-neighbor pitch of ∼ µ mand uses a low noise front end design achieving a projectedreadout noise of 14 electrons Root Mean Square (RMS). Theadvantage of using hexagonal over square pixels is that all thenearest neighbors of any given pixel are equivalent; in squarepixels, some immediate neighbors are closer than others. An-other similar ASIC for hybridization with pixelated CZT de-tectors is the High Energy X-ray Imaging Technology (HEX-ITEC) ASIC developed by Rutherford Appleton Laboratory.The HEXITEC ASIC features 6400 square pixels at a next-neighbor pitch of 250 µ m with an electronic readout noise of50 electrons RMS (Ryan et al., 2016; Baumgartner et al., 2016;Ryan et al., 2017).Our simulations model in detail the interactions of the in-cident photons, secondary photons and high-energy electronsgenerated in the CZT, and the ionization losses of the latter.The simulations furthermore model the drift and di ff usion of thenegative and positive charge carriers through the CZT, includ-ing the e ff ects of mutual repulsion of charge carriers of equalpolarity. This detailed treatment allows us to predict the prop-erties of the signals, including the pixel multiplicity, and the de-pendence of the pixel signals on where in the detector the freecharge carriers are generated. Earlier discussions of CZT de-1 a r X i v : . [ a s t r o - ph . I M ] F e b igure 1: Sketch showing how an energy deposition leads to the generation ofa free electron cloud that follows the applied electric field to the anode con-tacts, and widens owing to the e ff ects of di ff usion and repulsion of charges ofequal polarity. Our model captures the e ff ects of charge carriers being createdalong one or sometimes several photo-electron tracks, and accounts not onlyfor drifting electrons (shown here), but also for drifting holes (not shown). tector simulations can be found in (Benoit and Hamel, 2009;Kitaguchi et al., 2011; Ryan et al., 2017; Persson and Pelc,2019; Lai et al., 2019). Compared to the earlier study of smallpixel detectors of (Ryan et al., 2017), the shape of our chargeclouds evolve owing to charge carrier repulsion and di ff usion asthe clouds drift inside the detector. Furthermore, we extend thestudy from a pixel pitch of 250 µ m to smaller 150 µ m pixels.The rest of the paper is organized as follows. After describingthe detector simulation methodology in Section 2, we presentthe results of the simulations in Section 3. Our studies showthat the 1 mm thick detectors have a limited energy range overwhich they give excellent performance. We discuss the resultsand implications for the camera of a NuSTAR follow-up missionin Section 4.
2. Simulations of the CZT / ASIC Hybrid Detectors
X-rays impinging on a CZT detector interact via photoelec-tric, scattering, and pair production interactions. Photoelec-tric interactions dominate up to primary photon energies of E γ <
240 keV at which Compton scattering becomes dominant(assuming 40% Cd, 10% Zn and 50% Te). The photo-electronof a photoelectric e ff ect interaction loses most of its energy toionization. The ionization promotes electrons to the conduc-tion band, generating clouds of electrons and holes. Applyinga bias across the detector causes the charge carriers to drift andto induce the read-out signal. While drifting, the charge cloudsexpand due to the repulsion and attraction between charge car-riers and di ff use owing to spatial concentration gradients. Insmall-pixel detectors, the charge clouds can spread and inducecurrents over multiple pixels, resulting in charge sharing (Fig.1).The simulations consist of three parts: simulations of thephoton interaction and subsequent energy losses of the photo-electron, Compton electron, or produced pairs and their secon-daries, a simulation of the detector drift field, and charge cloudtracking and signal integration. Geant4
Simulations
The interaction of the photons with the 1 mm thick detectorare simulated with the
Geant4 simulation toolkit (CERN, 2019)at discrete photon energies. The resulting interactions and en-ergy depositions are stored for subsequent post-processing.The upper panel of Figure 2 shows the energies deposited inthe simulated CZT detector by a beam of 50 keV photons. Alarge fraction of 89.3% of the photons deposit their full energyin the detector. Some prominent escape peaks can be recog-nized. The peaks correspond to the initial energy of 50 keVminus the fluorescence photon energies. Secondary photonsfrom an earlier interaction may escape the detector, resultingin incomplete energy detection, as shown by the energy depo-sitions less than 50 keV. The lower panel of Figure 2 shows theenergy of the photons produced in the CZT and identifies sev-eral prominent X-ray lines of the Cd, Zn, and Te atoms. Theobjective of the optimization of the detector design is to recon-struct the deposited energy as well as possible. The energy es-caping the detector can, of course, not be recovered, and thuscontributes along the Fano factor limit to the theoretical bestpossible achievable energy resolution.
The electrostatic potential φ and electric field inside thedetector are inferred from solving Gauss’ law with Dirichletboundary conditions: ∇ · D = −∇ (cid:15) · ∇ φ − (cid:15) ∇ φ = . (1)Here, D is the electric displacement field, and (cid:15) ≈ (cid:15) is theelectric permittivity of CZT (Kitaguchi et al., 2011). Eq. (1) issolved on a three-dimensional discrete rectangular grid. Thedetector has a monolithic cathode in the z = z = d plane, where d is thethickness of the detector. The x and y directions are equivalentin terms of the grid resolution needed, so we set δ x = δ y (cid:44) δ z ,where δ x , δ y , and δ z denote the grid spacing in the x , y , and z directions, respectively. We expect the potential to closely re-semble that of a parallel plate capacitor throughout most of thedetector, so we take δ z to be relatively large compared to δ x and δ y . We use the finite di ff erence approximations d fdx = f ( x + h ) − f ( x − h )2 h + O ( h ) , (2) d fdx = f ( x + h ) − f ( x ) + f ( x − h ) h + O ( h ) (3)to solve Eq. (1) with the Successive Overrelaxation Method(SOR) (Press et al., 2007). In each iteration, the electric po-tential is updated to the average of the surrounding values, in-cluding a certain amount of “overshooting” to accelerate con-vergence: φ (cid:55)→ ωφ ∗ + (1 − ω ) φ, (4)where ω is called the overrelaxation factor and φ ∗ is calculatedby solving for the potential at the center grid point after substi-tuting Eqs. (2) and (3) into Eq. (1). The method converges for2 nergy deposited [keV] E v en t s Photon energy [keV] C oun t s All secondary photonsCompton scatteringPhotoabsorption
Zn K α Zn K β Cd K Cd K Te KTe KTe K α β β αβ Figure 2:
Top:
Distribution of the total energy deposited by 50 keV photons inthe CZT detectors. In this simulation of 10 events, 89.3% have the full 50 keVdeposited. For the remaining events, some energy escapes the detector, leadingto substantially smaller total energy deposits. Bottom:
For the same incident 50keV photons as shown in the upper panel, the lower panel presents the distribu-tion of the energies of photons produced in the CZT detector, either throughCompton scattering, or, following photoelectric absorption and the inelasticscattering of the photo-electron, through the emission of fluorescent photons.Prominent fluorescence lines are labeled. values of ω between 1 and 2. The running time can be reducedby starting with an initial guess that is close to the expected po-tential. The final potential is expected to be close to that of aparallel plate capacitor, so the starting configuration was a sim-ple gradient in z .The error is calculated using the norm of an error vector e ,where e i = ( ∇ · D ) i , where ( ∇ · D ) i ( ∇ · D calculated at the i th gridpoint) is calculated using Eq. (1) and the discrete derivatives.For a tolerance ε and G grid points, we consider the simulationconverged if | e | < ε G . For our simulations, we chose a toleranceof 10 − .This paper presents the results of simulations for a singledetector geometry as described by Table 1. We use periodicboundary conditions in the x and y directions and a groundedplane beyond the anode at z = d , where d is the detector thick-ness. The last boundary condition is imposed to simulate thepotential inside and outside of the detector so that the electricfield between pixels can be calculated. The results for this sim-ulation are shown in Fig. 3. For each event, the
Geant4 simulations give us the locationsof the ionization energy deposits in the detector, which we o ff -set to randomize the incident photon over a rectangular unit cellcentered on a single pixel. We use this information to generateelectrons and holes that are free to move through the detector.Energy depositions which occur su ffi ciently close to one an-other are merged and treated as a single deposition (discussedfurther in 2.3.2) while unmerged depositions are treated inde-pendently.Subsequently, we track the motion of these electrons andholes through the detector accounting for the local electric field(caused by the applied detector bias), as well as charge carrierdi ff usion (a stochastic process) and electron-electron repulsion.We group charge carriers into small bundles (also referred toin this paper as “charge elements”) which are tracked as a sin-gle unit, with electron and hole bundles being pulled in oppo-site directions by the local electric field, and individual chargebundles experiencing di ff erent di ff usion and repulsion relateddisplacements. The photo-electrons of some events cause theemission of fluorescent photons, that, when being absorbed,give rise to secondary photo-electrons. Our treatment allowsus to track the free charge carriers from all these processes. We evolve the drift velocity with the equation v d = ± µ E = ∓ µ ∇ φ, (5)where µ is the carrier mobility and is defined to be positive forboth electrons and holes. The upper signs are for holes and thelower signs are for electrons. Table 1 lists the mobilities used inthe simulations with subscripts e and h for electrons and holes,respectively. We calculate the electric field at the grid pointsas described above and use a trilinear interpolation to calculatethe electric field between grid points. The resulting change inposition per integration step is calculated using Euler’s method: δ r = v d δ t . ff usion and Repulsion We implement the expansion of a carrier cloud through dif-fusion and repulsion following Benoit and Hamel (Benoit andHamel, 2009). We neglect the attraction between charge carri-ers of opposite polarity, which may slow down the initial chargeseparation. For an energy deposition E d and mean ionizationenergy per electron hole pair E , an average of N = E d / E electron-hole pairs are created. The actual number of electron-hole pairs created N is chosen from a Gaussian distribution withmean N and σ = √ N F , where F is the Fano factor. For CZT,this is F = .
089 (Table 1). To improve performance, the cloudof N charge carriers is broken down into n charge elements,each containing N / n charge carriers. The initial distribution ofthese charge elements is modeled by a spherically symmetricGaussian with RMS radius R p = AE d (cid:32) − B + CE d (cid:33) , (6)3 igure 3: Two-dimensional slices of the three-dimensional simulated potentials. This geometry features a 1 mm thick detector, 150 µ m center-to-center pitch with15 µ m spacing between pixels, and a −
150 V bias. The bottom slices (vertical slices through the center pixels) only show the potential inside the detector; however,there is additional vacuum simulated up to z = Left : Slices of the electricpotential. This is the drift field which pulls electrons toward the pixelated anode side and holes towards the cathode side of the detector.
Right : Slices of theweighting potential. This is the field that is integrated along the carriers’ trajectories to calculate the induced signal. x , y δ x = δ y /
750 mmGrid spacing in z δ z /
50 mmDielectric constant (cid:15) (cid:15) Kitaguchi et al. (2011)Time step δ t . E . F µ e / V · s Ari˜no-Estrada et al. (2014)Electron trapping time τ e . µ s Ari˜no-Estrada et al. (2014)Hole mobility µ h
110 cm / V · s Ari˜no-Estrada et al. (2014)Hole trapping time τ h . µ s Ari˜no-Estrada et al. (2014)Electron di ff usion constant D e
26 cm / sHole di ff usion constant D h / sDetector thickness – 1 mmPixel pitch – 150 µ mPixel spacing – 15 µ mCathode bias – −
150 V
Table 1: Constants and detector parameters for the simulation. where A = . µ m / keV, B = .
98, and C = .
003 keV − arematerial-specific constants (Wohl et al., 1984). In our simu-lations, this is not only used to parameterize the initial chargedistribution, but it is also used to determine whether two cloudsare close enough to a ff ect each others’ di ff usion and repulsion,in which case the energy depositions are merged and the twoclouds are approximated by a single cloud located at the centerof mass. The merging criteria was determined based on obser-vations of the degree to which charge clouds expanded from theinitial distribution in the same simulations.The density gradient within a cloud causes di ff usion of thecharge elements and the electric field created by the chargescauses repulsion. These a ff ect the charge density ρ accordingto ∂ρ∂ t = D ∇ ρ − µ ∇ · ( ρ E ) , (7)where D is the di ff usion coe ffi cient, µ is the carrier mobility,and E here is the electric field produced by the charges in thecloud (Benoit and Hamel, 2009). The values of D used in oursimulation for electrons and holes are listed in 1 with subscripts e and h , respectively, and were derived using the Einstein rela-tion for charged particles at room temperature: D = µ k B Tq . (8)Benoit and Hamel showed that for an ellipsoidal Gaussiancharge distribution with σ = ( σ x , σ y , σ z ), the time evolutionof the distribution is described by ∂ σ ( t ) ∂ t = D (cid:48) , (9)where D (cid:48) is the vectorial e ff ective di ff usion coe ffi cient D (cid:48) = (cid:32) D + λ σ x σ y σ z , D + λ σ y σ x σ z , D + λ σ z σ x σ y (cid:33) , (10)with: λ ≡ eN µ √ π(cid:15) . This e ff ective di ff usion coe ffi cient encapsulates the e ff ects ofboth di ff usion and repulsion. At each time step, σ and D (cid:48) arerecalculated and each charge element is displaced by a randomwalk in x , y , and z by distances selected from a Gaussian pa-rameterized by σ i = (cid:112) D (cid:48) i δ t , where δ t is the size of the timestep. While the charge carriers are moving in the detector, theymay encounter impurities and recombine in the material, or aretrapped and released on time scales longer than the shaping timeof the readout electronics. When this occurs, we e ff ectivelylose the charge as it no longer contributes to the signal. Weaccount for trapping by reducing the amount of charge presentaccording to: q ( t ) = q e − t /τ , (11)where q is the initial charge at time t = t is the time sincethe energy was deposited, and τ is the carrier lifetime, whichquantifies trapping as a bulk property of the cloud. The valuesof τ used in the simulations are listed in Table 1 with subscripts e and h electrons and holes, respectively. Trapping is caused bycrystal defects such as Te precipitates (e.g. Bolke et al., 2017;Zhang et al., 2018; Winkler et al., 2019; Kim et al., 2019; Yaki-mov et al., 2019; Brovko and Ruzin, 2020; McCoy et al., 2020).Owing to the lack of information about the spatial distributionand size of charge trapping sites, we neglect the statistical fluc-tuations caused by the charge trapping mechanisms. Detailedcomparisons of simulations as those presented here and mea-sured data could be used to constrain these material properties. Charged particles moving near an electrode induce a chargeon the electrode. Shockley showed a way to quantify this withthe Shockley-Ramo Theorem (Shockley, 1938; He, 2001): q ind = − q ∆ φ wp , (12)5here ∆ φ wp is the change in weighting potential between twopoints in the charge q ’s trajectory and q ind is the charge inducedon the electrode. The weighting potential is a unit-less poten-tial found by setting the electrode for which we want to cal-culate the induced charge to 1 and all others to 0. With theseboundary conditions, the procedure described in 2.2 is followedto calculate the weighting potential. The right panels of Figure3 show that most of the change in weighting potential occursnear the pixels. This is the well-known small pixel e ff ect (Bar-rett et al., 1995; He, 2001): as the signal is mostly generatednear the pixels, it becomes largely independent of the locationof the primary interaction.To simulate the currents read by the electrodes, we use analternate form of Eq. (12): I ind = q v · E wp , (13)where v is the instantaneous velocity of the charge (consideringboth drift and di ff usion) computed from the change of locationin this time step, and E wp is the “electric field” resulting fromthe weighting potential. These are implemented as the averagevelocity over the whole time step and the trilinear interpolatedweighting potential.For each event, there may be several energy depositions fol-lowing the initial photon interaction in the crystal, includingelastic and inelastic photon scattering, and the ionization alongthe track of energetic electrons. Following the design of theHEXID ASIC, we assume that the electronics read out all pix-els with an energy exceeding the trigger threshold as well asthe immediate neighbors of these pixels (even if the signals inthe neighboring pixels do not exceed the trigger threshold). Wewill see below that this scheme leads to excellent energy resolu-tions at lower photon energies ( < ∼
60 keV). At higher energies,energy escaping the detector or traveling to pixels further awaystarts to become an issue, and does deteriorate the detectors’energy resolutions. We analyzed the data for the bipolar inte-gration of the signal (read out of the integrated negative andpositive charge).
3. Results
In this section, we discuss methods to reconstruct the energyof the incident photon, and the location of the primary interac-tion. We will first discuss the results obtained in the absenceof readout noise, and the show how they change as we add thenoise expected for the HEXID ASIC.
The procedure in Section 2 was followed for a detector withthe boundary conditions described in 2.2 and with 22 . r = Q neighbors Q center , (14)where Q center is the charge induced on the center pixel (the pixelwith the largest signal), and Q neighbors is the total charge induced Figure 4: The panel shows the ratio r of the charge induced on neighbor pixelsdivided by the charge induced on the brightest pixel (Eq. (14)) as a function ofthe distance of the initial charge deposition from the center of the brightest pixelfor incident 22.9 keV photons. The initial photon positions are randomized overa rectangular unit cell. Due to the hexagonal pixel geometry, the pixel edge maybe located between 1 / / √ . on its six neighbors. As expected, the charge ratio r increaseswith the distance from the center of the pixel (Fig. 4).We see that adding up the charge from the center pixel whichexceeds a certain threshold value and all its adjacent pixels isimportant for achieving good energy resolution. This require-ment means that the total readout noise is given by the quadraticsum of the readout noise of a total of between one and sevenpixels. Fig. 5 shows the total induced charge on the center pixeland its nearest neighbors plotted against the charge ratio. Thesum signal decreases (increases in magnitude) with increasingcharge ratio, which may be indicative of small negative inducedcharges from farther pixels for which the signal was not calcu-lated.To correct for this di ff erence in charge, a multiplicative cor-rection histogram was made from applying cuts at − . − orrectedEntries 9554Mean 22.87
21 21.5 22 22.5 23 23.5 24 24.5 25Reconstructed Energy (keV)0100200300400500600700 C oun t s CorrectedEntries 9554Mean 22.87
CorrectedUncorrectedPhoton energy
Figure 6: The reconstructed energies from the simulations for 22 . r fromEquation (14). The black line indicates the incident photon energy. structed energy is corrected by multiplying the raw integratedcharge by the value of this correction histogram correspondingto the event’s charge ratio.Figure 6 shows the energies reconstructed from charge in-tegration both before and after multiplicative correction. Thecorrected peak has a full width at half maximum (FWHM) of0 .
260 keV. The energy spectrum shown here does not yet in-clude the electronic readout noise.The readout Equivalent Noise Charge (ENC) depends on thedetector capacitance and the readout electronics. The pixel ca-pacitance can be calculated from two maps of the potential cal-culated for di ff erent bias voltages. Integrating the electric fieldaround the pixel gives the charge on the pixel via Gauss’ law.The di ff erence ∆ V of the two bias voltages and the di ff erence ∆ q of the inferred charges gives the capacitance according to: C = ∆ q ∆ V . (15)For this 1 mm thick CZT detector with with 150 µ m pix-els, the per-pixel capacitance is 6 .
94 pF. For the HEXID ar-chitecture, this capacitance leads to a conservatively-estimatednoise of 14-electron ENC. Figure 7 shows the results of theenergy reconstruction with this noise included. The FWHMis 0 .
435 keV. The same correction histogram as before wasused. The corrected energies’ peak is still centered at the pho-ton energy, which is expected given that the Gaussian was cen-tered about 0, and that the noise is small compared to the totalcharge across all pixels, which contributes to minimal shifts inthe charge ratio and therefore the correction factor.We tested if a single correction histogram (derived for22 . . . . . .
350 keV. For 67 . . CorrectedEntries 9554Mean 22.89
21 21.5 22 22.5 23 23.5 24 24.5 25Reconstructed Energy [keV]050100150200250300350400450 C oun t s CorrectedEntries 9554Mean 22.89
CorrectedUncorrectedPhoton energy
Figure 7: The reconstructed energies with a 14 electron ENC. The same cor-rection histogram as that used for Fig. 6 was used.
Photonenergy[keV] Fano[keV] LocationDepen-dence[keV] ENC[keV] Total[keV]4.8 0.104 0.017 0.334 0.35022.9 0.228 0.125 0.349 0.43567.9 0.398 0.376 0.607 0.81578.4 0.421 1.014 0.756 1.333122.1 0.525 3.995 2.421 4.701158.4 0.598 7.818 0 7.841
Table 2: The resolution (FWHM) of the reconstructed energy from each sourceof noise: Fano noise, dependence of the induced charge on the locations ofthe energy deposition, electrical readout noise (ENC), and total noise. The158 . . the incident photon energy. The reconstructed energies weremultiplied by an additional correction factor to push the peakof the energy spectrum to the true X-ray energy. These fac-tors were less than 1%, so they did not significantly impactthe energy resolution. Note that the average values shown inthe figures are lower than peak location due to the presence ofthe low-energy tails. The FWHM calculated from the binnedspectra were 0 .
815 keV for the 67 . .
333 keV for the 78 . . . Co and Ni, re-spectively. The energy spectra show pronounced low-energytails. Two e ff ects contribute to this e ff ect: some of the pho-tons interact close to the anode side of the detector, so thatthe drifting electrons induce little charge before impinging onthe anodes (see Fig. 3, Eq. (12)). The second e ff ect is thatscattered photons are only absorbed after traveling beyond thenext neighbor pixels, or leave the detector altogether. In bothcases, their energy does not count towards the reconstructed7 orrectedEntries 14240Mean 4.801 C oun t s CorrectedEntries 14240Mean 4.801
CorrectedUncorrectedPhoton energy
CorrectedEntries 9146Mean 67.07
62 64 66 68 70 72 74Reconstructed Energy [keV]020406080100120 C oun t s CorrectedEntries 9146Mean 67.07
CorrectedUncorrectedPhoton energy
CorrectedEntries 8258Mean 77.08
72 74 76 78 80 82 84 86Reconstructed Energy [keV]020406080100120 C oun t s CorrectedEntries 8258Mean 77.08
CorrectedUncorrectedPhoton energy
Figure 8: The reconstructed energies for 4 . top ), 67 . middle ), and78 . bottom ) photon events with 14-electron ENC. All used the correctionhistogram from the 22 . . . CorrectedEntries 8260Mean 74.19 C oun t s CorrectedEntries 8260Mean 74.19
CorrectedUncorrectedPhoton energy
CorrectedEntries 7475Mean 92.59 C oun t s CorrectedEntries 7475Mean 92.59
CorrectedUncorrectedPhoton energy
Figure 9: The reconstructed energies for 122 . top ) and 158 . bot-tom ) photon events with 14-electron ENC. There are significant energy lossesas evidenced by the high level of reconstructed energies down to 0 keV. Thesereconstructed energies were multiplied by a small ( ∼
1) correction factor to shiftthe peak to the true photon energy. energy. The 122 . . ff ects) are 4 . . r does not lead to a marked improvement of the energyresolutions. We therefore only used the raw integrated chargeand a peak-shifting multiplicative factor close to one to recon-struct these energies. Developing and testing a more sophisti-cated Maximum Likelihood energy reconstruction is outside ofthe scope of this paper. Most photons do not interact with thedetector at all; only 41% of 122 . . . . In the next step, we reconstruct the original photon posi-tion using the charge-weighted average position of the brightestpixel and its six nearest neighbors. The simulations include thereadout noise of 14-electron ENC.Figure 10 shows the absolute di ff erence in the reconstructed x and y position of the incident photon using the weighted av-erage of the pixels’ center coordinates. We first discuss the re-sults for 4 . . a)(b)(c)(d)(e)(f) Figure 10: The absolute error in the reconstructed x and y position of the incident photon using the energy-weighted average of the integrated charge on the brightestpixel and its nearest neighbors ( left ) and the squared distance ∆ r between the reconstructed position and incident photon ( right ) for 4 . . . . . . ff ects from noise, as in the 4 . ∆ r =
20 and 30 µ m. igure 11: The errors in reconstructed photon positions for 4 . top ) and22 . bottom ) zoomed to ± µ m in either direction. These account forover 99% of all reconstructed positions at these energies. (0 ,
0) for both energies that indicate that the reconstruction isgenerally accurate at these energies. In the reconstructions forboth energies, there are a few reconstructed positions that areconsiderably farther away ( > ff ect is the ENC for the 4 . . . µ m from the coordinates of theincident photon in both the x and y directions; for the 4 . ff erent at higher energies (Fig.10, lower four panels). The increased e ff ect of charge sharingleads to a better position reconstruction for some events andthus to a more centrally peaked distance distribution. However,as scattered photons can travel farther away from the location ofthe first interaction, there is also a larger tail towards larger dis-placements. The net e ff ect is that the HPD of the reconstructedpositions is largely independent of the energy of the primaryphoton (Table 3). Photon energy [keV] PositionReconstruction HPD[ µ m]4.8 41.822.9 34.567.9 43.478.4 41.0122.1 46.4158.4 37.7 Table 3: The spatial resolution (HPD) of the reconstructed positions from thesimulated incident photons.
4. Discussion
In this paper, we present simulations of 1 mm thick CZT de-tectors with hexagonal pixels at an extremely small pixel pitchof 150 µ m. The detector simulations account for the spatiallydistributed generation of free charge carriers in the detector, andthe drift and di ff usion of the charge of both polarities. The sim-ulations furthermore account for the anticipated charge resolu-tion of the HEXID3 ASIC. We have shown that the sum of thesignals of the brightest pixel and the adjacent pixels and the ra-tio of the sum of the charge in the neighbor pixel divided by thecharge of the brightest pixel, give FWHM energy resolutionsof 350 eV at 4 . . . .
333 keV at 78 . . . . . µ m for all theenergies we simulated (4.8-158 . / ASIC systems have been fabri-cated.The results presented here can be compared with previ-ously published simulated and experimental results. Benoit andHamel (2009) for example simulate a 7 . µ m and ob-tain good agreement between simulated and experimental data.They report energy resolutions of approximately 7 keV and14 keV FWHM for the 59 . Am line and 122 . Coline, respectively. The thick detectors suppress the low-energytail evident in the energy spectra presented in this paper.Ryan et al. (2017) present measurement results obtained withthe HEXITEC CZT / ASIC hybrids which feature pixels at anext-neighbor pitch of 250 µ m on 1 mm thick CZT detectors,and compare the experimental results with simulated results.Rather than modeling the spatially distributed energy deposi-tions following the impact of the primary photon and the evo-lution of the charge cloud in the detector as done in our work,Ryan et al. used a phenomenological parameterization of thesize of the charge clouds. Using a 2-D Gaussian with a width10 = µ m, they were able to model the shape of the energyspectrum observed for a ∼
20 keV X-ray beam from an X-raygun. Our approach is more general, and can be used over awider range of energies.The interested reader may consult (Iniewski et al., 2007;Rana et al., 2009; Kitaguchi et al., 2011; Yin et al., 2011, 2013,2014; Veale et al., 2014; Mont´emont et al., 2014; Ocampo Gi-raldo et al., 2018; Khalil et al., 2018) for discussions of chargesharing in CZT detectors, and (Zhang et al., 2004; Benoit andHamel, 2009; De Geronimo et al., 2008; Kim et al., 2011;Zhang et al., 2012; Beilicke et al., 2013; Yin et al., 2014; Kimet al., 2014; Wahl et al., 2015; Chen et al., 2018) for discussionof CZT detectors of di ff erent thicknesses and pixel sizes.Detectors with pixels at 150 µ m pixel pitch, as the ones dis-cussed in this paper, would be well suited for a NuSTAR follow-up mission with arcsecond angular resolution and a
NuSTAR -like focal length of 10 m. For these parameters, an HPD of 5 (cid:48)(cid:48) corresponds to a 242 µ m focal spot. A pixel pitch of 150 µ mwould thus enable an oversampling factor of 1.6. A longer fo-cal length of 20 m and an HPD of 15 (cid:48)(cid:48) , as proposed for HEX-P(Madsen et al., 2018), the pixel diameter would correspond to aspot diameter of 1 . ∼
70 keV and above, the 1 mm thick detectorsstudied in this paper start to become transparent, and the energyspectra start to develop an increasingly pronounced low-energytail. The tail results from a combination of photons interact-ing close to the detector anodes so that electrons induce littlecharge before impinging on the anodes, and Compton scatteredphotons traveling beyond the next neighbor pixels or escapingthe detector. Thicker detectors suppress both e ff ects, but lead tolonger drift paths and thus to additional charge spreading andlarger pixel multiplicities – e ff ects that adversely a ff ect the en-ergy resolution. Covering the broad energy range from ∼ ∼
160 keV or higher as envisioned for
HEX-P may require alayered detector, e.g. a front layer of thin ( ∼ ∼ ffi ciency and excellent resolutions.Note that several alternatives to CZT detectors are currentlybeing developed. A possible alternative for finely-pixelatedCZT detectors are Thallium Bromide (TlBr) detectors. Thehigh atomic number of Thallium (81) make TlBr more e ffi -cient for photoelectric interactions than CZT, and Kim et al.(2020) report sub-1% energy resolutions. Germanium basedCharge Coupled Devices (Ge-CCDs) may be another competi-tor, but still su ff er from yield issues (Leitz et al., 2019). Weare currently evaluating the gamma-ray detectors made of tinabsorbers and Transition Edge Sensors (TES) developed by theNational Institute of Standards and Technology (NIST) (Ben-nett et al., 2012; Mates et al., 2017). The microcalorimeterdetectors achieve superior energy resolutions (i.e. 53 eV at97 keV) than solid state detectors. For the time being, the draw-back of the TES gamma-ray detectors are spatial resolutions onthe order of ∼ ∼
100 keV o ff ering a unique combination of operation atroom temperatures, high stopping power, high photo-electric toCompton scattering cross sections, sub-mm spatial resolutions,and good energy resolutions. Acknowledgements
We thank Grzegorz Deptuch, Gabriella Carini, and ShaoruiLi for their work on the HEXID ASIC, as well as the McDon-nell Center for the Space Sciences at Washington Universityin St. Louis for its support. We thank Richard Bose and An-drew West for designing a HEXID readout system and HEXIDphotomasks. HK acknowledges NASA support under grants80NSSC18K0264 and NNX16AC42G.
References
Ari˜no-Estrada, G., Chmeissani, M., de Lorenzo, G., Kostein, M., Puigdengoles,C., Garc´ıa, J., Cabruja, E., 2014. Measurement of mobility and lifetime ofelectrons and holes in a schottky CdTe diode. Journal of Instrumentation9, C12032–C12032. URL: https://doi.org/10.1088%2F1748-0221%2F9%2F12%2Fc12032 , doi: .Barrett, H.H., Eskin, J.D., Barber, H.B., 1995. Charge transport in ar-rays of semiconductor gamma-ray detectors. Phys. Rev. Lett. 75, 156–159. URL: https://link.aps.org/doi/10.1103/PhysRevLett.75.156 , doi: .Baumgartner, W.H., Christe, S.D., Ryan, D.F., Inglis, A.R., Shih, A.Y., Gre-gory, K., Wilson, M., Seller, P., Gaskin, J., Wilson-Hodge, C., 2016. TheHEXITEC hard x-ray pixelated CdTe imager for fast solar observations, in:Holland, A.D., Beletic, J. (Eds.), High Energy, Optical, and Infrared Detec-tors for Astronomy VII, p. 99151D. doi: .Beilicke, M., De Geronimo, G., Dowkontt, P., Garson, A., Guo, Q., Lee, K.,Martin, J., Krawczynski, H., 2013. Performance of pixelated CZT detec-tors as a function of pixel and steering grid layout. Nuclear Instrumentsand Methods in Physics Research A 708, 88–100. doi: .Bennett, D.A., Horansky, R.D., Schmidt, D.R., Hoover, A.S., Winkler, R.,Alpert, B.K., Beall, J.A., Doriese, W.B., Fowler, J.W., Fitzgerald, C.P.,Hilton, G.C., Irwin, K.D., Kotsubo, V., Mates, J.A.B., O’Neil, G.C., Rabin,M.W., Reintsema, C.D., Schima, F.J., Swetz, D.S., Vale, L.R., Ullom, J.N.,2012. A high resolution gamma-ray spectrometer based on superconductingmicrocalorimeters. Review of Scientific Instruments 83, 093113–093113–14. doi: .Benoit, M., Hamel, L., 2009. Simulation of charge collection pro-cesses in semiconductor CdZnTe γ -ray detectors. Nuclear In-struments and Methods in Physics Research Section A: Accelera-tors, Spectrometers, Detectors and Associated Equipment 606, 508 –516. URL: , doi: https://doi.org/10.1016/j.nima.2009.04.019 .Boggs, S.E., Harrison, F.A., Miyasaka, H., Grefenstette, B.W., Zoglauer,A., Fryer, C.L., Reynolds, S.P., Alexander, D.M., An, H., Barret,D., Christensen, F.E., Craig, W.W., Forster, K., Giommi, P., Hai-ley, C.J., Hornstrup, A., Kitaguchi, T., Koglin, J.E., Madsen, K.K.,Mao, P.H., Mori, K., Perri, M., Pivovaro ff , M.J., Puccetti, S., Rana,V., Stern, D., Westergaard, N.J., Zhang, W.W., 2015. 44ti gamma-ray emission lines from sn1987a reveal an asymmetric explosion.Science 348, 670–671. URL: https://science.sciencemag.org/content/348/6235/670 , doi: , arXiv:https://science.sciencemag.org/content/348/6235/670.full.pdf .Bolke, J., O’Brien, K., Wall, P., Spicer, M., G´elinas, G., Beaudry, J.N., Alexan-der, W.B., 2017. Measuring Te inclusion uniformity over large areas forCdTe / CZT imaging and spectrometry sensors, in: SPIE proceedings, p.104231M. doi: .Brovko, A., Ruzin, A., 2020. Study of material uniformity in high-resistivityCd1- x Zn x Te and Cd1- x Mn x Te crystals. Nuclear Instruments and Methodsin Physics Research A 958, 161996. doi: . ERN, 2019. Geant4. URL: https://geant4.web.cern.ch/ .Chen, H., Li, H., Reed, M.D., Sundaram, A.G., Eger, J., Hugg, J.W., Ab-baszadeh, S., Li, M., Montemont, G., Verger, L., Zhu, Y., He, Z., 2018.Development of large-volume high-performance monolithic CZT radiationdetector, in: Hard X-Ray, Gamma-Ray, and Neutron Detector Physics XX,p. 107620N. doi: .De Geronimo, G., Vernon, E., Ackley, K., Dragone, A., Fried, J., O’Connor,P., He, Z., Herman, C., Zhang, F., 2008. Readout ASIC for 3D Position-Sensitive Detectors. IEEE Transactions on Nuclear Science 55, 1593–1603.doi: .Gaskin, J., Elsner, R., Ramsey, B., Wilson-Hodge, C., Tennant, A., Christe,S., Shih, A., Kilaru, K., Swartz, D., Seller, P., Wilson, M., Stuchlik, D.,Weddendorf, B., 2015. Superhero: Design of a new hard-x-ray focusingtelescope, in: 2015 IEEE Aerospace Conference, pp. 1–15. doi: .Grefenstette, B.W., Fryer, C.L., Harrison, F.A., Boggs, S.E., DeLaney, T., Lam-ing, J.M., Reynolds, S.P., Alexander, D.M., Barret, D., Christensen, F.E.,Craig, W.W., Forster, K., Giommi, P., Hailey, C.J., Hornstrup, A., Kitaguchi,T., Koglin, J.E., Lopez, L., Mao, P.H., Madsen, K.K., Miyasaka, H., Mori,K., Perri, M., Pivovaro ff , M.J., Puccetti, S., Rana, V., Stern, D., Wester-gaard, N.J., Wik, D.R., Zhang, W.W., Zoglauer, A., 2017. The Distributionof Radioactive Ti in Cassiopeia A. The Astrophyical Journal 834, 19.doi: , arXiv:1612.02774 .Grefenstette, B.W., Harrison, F.A., Boggs, S.E., Reynolds, S.P., Fryer, C.L.,Madsen, K.K., Wik, D.R., Zoglauer, A., Ellinger, C.I., Alexand er, D.M.,An, H., Barret, D., Christensen, F.E., Craig, W.W., Forster, K., Giommi, P.,Hailey, C.J., Hornstrup, A., Kaspi, V.M., Kitaguchi, T., Koglin, J.E., Mao,P.H., Miyasaka, H., Mori, K., Perri, M., Pivovaro ff , M.J., Puccetti, S., Rana,V., Stern, D., Westergaard, N.J., Zhang, W.W., 2014. Asymmetries in core-collapse supernovae from maps of radioactive Ti in CassiopeiaA. Nature506, 339–342. doi: , arXiv:1403.4978 .Harrison, F.A., Craig, W.W., Christensen, F.E., Hailey, C.J., Zhang, W.W.,Boggs, S.E., Stern, D., Cook, W.R., Forster, K., Giommi, P., Grefen-stette, B.W., Kim, Y., Kitaguchi, T., Koglin, J.E., Madsen, K.K., Mao, P.H.,Miyasaka, H., Mori, K., Perri, M., Pivovaro ff , M.J., Puccetti, S., Rana, V.R.,Westergaard, N.J., Willis, J., Zoglauer, A., An, H., Bachetti, M., Barri`ere,N.M., Bellm, E.C., Bhalerao, V., Brejnholt, N.F., Fuerst, F., Liebe, C.C.,Markwardt, C.B., Nynka, M., Vogel, J.K., Walton, D.J., Wik, D.R., Alexan-der, D.M., Cominsky, L.R., Hornschemeier, A.E., Hornstrup, A., Kaspi,V.M., Madejski, G.M., Matt, G., Molendi, S., Smith, D.M., Tomsick, J.A.,Ajello, M., Ballantyne, D.R., Balokovi´c, M., Barret, D., Bauer, F.E., Bland-ford, R.D., Brandt, W.N., Brenneman, L.W., Chiang, J., Chakrabarty, D.,Chenevez, J., Comastri, A., Dufour, F., Elvis, M., Fabian, A.C., Farrah,D., Fryer, C.L., Gotthelf, E.V., Grindlay, J.E., Helfand, D.J., Krivonos,R., Meier, D.L., Miller, J.M., Natalucci, L., Ogle, P., Ofek, E.O., Ptak,A., Reynolds, S.P., Rigby, J.R., Tagliaferri, G., Thorsett, S.E., Treister,E., Urry, C.M., 2013. The Nuclear Spectroscopic Telescope Array (NuS-TAR) High-energy X-Ray Mission. The Astrophyical Journal 770, 103.doi: , arXiv:1301.7307 .He, Z., 2001. Review of the Shockley-Ramo Theorem and its Applicationin Semiconductor Gamma-ray Detectors. Nuclear Instruments and Meth-ods in Physics Research, Section A: Accelerators, Spectrometers, Detectorsand Associated Equipment 463, 250–267. doi: .Iniewski, K., Chen, H., Bindley, G., Kuvvetli, I., Budtz-Jorgensen, C., 2007.Modeling charge-sharing e ff ects in pixellated czt detectors, in: 2007 IEEENuclear Science Symposium Conference Record, pp. 4608–4611. doi: .Khalil, M., Dreier, E.S., Kehres, J., Jakubek, J., Olsen, U.L., 2018. Sub-pixel resolution in CdTe Timepix3 pixel detectors. Journal of Syn-chrotron Radiation 25, 1650–1657. URL: https://doi.org/10.1107/S1600577518013838 , doi: .Kim, E., Kim, Y., Bolotnikov, A.E., James, R.B., Kim, K., 2019. De-tector performance and defect densities in CdZnTe after two-step anneal-ing. Nuclear Instruments and Methods in Physics Research A 923, 51–54.doi: .Kim, H., Ogorodnik, Y., Kargar, A., Cirignano, L., Thrall, C.L., Koehler, W.,O’Neal, S.P., He, Z., Swanberg, E., Payne, S.A., Squillante, M.R., Shah,K., 2020. Thallium Bromide Gamma-Ray Spectrometers and Pixel Arrays.Frontiers in Physics 8, 55. doi: .Kim, J.C., Anderson, S.E., Kaye, W., Zhang, F., Zhu, Y., Kaye, S.J., He, Z., 2011. Charge sharing in common-grid pixelated CdZnTe detectors. NuclearInstruments and Methods in Physics Research A 654, 233–243. doi: .Kim, J.C., Kaye, W.R., He, Z., 2014. Signal modeling of charge sharing e ff ectin simple pixelated CdZnTe detector. Journal of Korean Physical Society64, 1336–1345. doi: .Kitaguchi, T., Grefenstette, B.W., Harrison, F.A., Miyasaka, H., Bhalerao, V.B.,Cook, Walter R., I., Mao, P.H., Rana, V.R., Boggs, S.E., Zoglauer, A.C.,2011. Spectral calibration and modeling of the NuSTAR CdZnTe pixel de-tectors. volume 8145 of Society of Photo-Optical Instrumentation Engineers(SPIE) Conference Series . p. 814507. doi: .Krawczynski, H., Tueller, J., Barthelmy, S., Schnittman, J., Zhang, W., Kro-lik, J., Baring, M.G., Treister, E., Mushotzky, R., Beilicke, M., Buckley, J.,Cowsik, R., Israel, M., 2012. The black hole evolution and space time (best)observatory. arXiv:1205.3691 .Lai, X., Cai, L., Zimmerman, K., Kaul, M., Zhan, X., Qiang, Y., Veale, M.,Thompson, R., 2019. CZT modeling for photon counting computer tomog-raphy, in: SPIE proceedings, p. 109484G. doi: .Leitz, C.W., Zhu, M., Rabe, S., Burke, B., Young, D., O’Mara, D., Prigozhin,I., Ryu, K., Cooper, M., Reich, R., Johnson, K., Cook, M., Stull, C.,Zarr, S., 2019. Towards megapixel-class germanium charge-coupled de-vices for broadband x-ray detectors, in: SPIE Proceedings, p. 1111802.doi: .Li, S., De Geronimo, G., Fried, J., Pinelli, D.A., Kuczewski, A., Peter Siddons,D., Beheshtipour, B., Bohse, R., Krawczynski, H., 2017. Hexid2: A low-power, low-noise pixel readout asic for hyperspectral energy-resolving x-rayimaging detectors, in: 2017 IEEE Nuclear Science Symposium and MedicalImaging Conference (NSS / MIC), pp. 1–4. doi: .Li, S., De Geronimo, G., Giacomini, G., Fried, J., Pinelli, D.A., Singh, B.,Miller, S., Nagarkar, V.V., 2018. Pd-hexid1: A low-power, low-noise pixelreadout asic for pixelated-scintillator-based x-ray detectors, in: 2018 IEEENuclear Science Symposium and Medical Imaging Conference Proceedings(NSS / MIC), pp. 1–4. doi: .Madsen, K.K., Harrison, F., Broadway, D., Christensen, F.E., Descalle, M.,Ferreira, D., Grefenstette, B., Gurgew, D., Hornschemeier, A., Miyasaka,H., Okajima, T., Pike, S., Pivovaro ff , M., Saha, T., Stern, D., Vogel, J.,Windt, D., Zhang, W., 2018. Optical instrument design of the high-energyx-ray probe (HEX-P), in: SPIE Proceedings, p. 106996M. doi: .Mates, J.A.B., Becker, D.T., Bennett, D.A., Dober, B.J., Gard, J.D., Hays-Wehle, J.P., Fowler, J.W., Hilton, G.C., Reintsema, C.D., Schmidt, D.R.,Swetz, D.S., Vale, L.R., Ullom, J.N., 2017. Simultaneous readout of 128X-ray and gamma-ray transition-edge microcalorimeters using microwaveSQUID multiplexing. Applied Physics Letters 111, 062601. doi: .McCoy, J.J., Kakkireni, S., G´elinas, G., Gara ff a, J.F., Swain, S.K., Lynn, K.G.,2020. E ff ects of excess Te on flux inclusion formation in the growth ofcadmium zinc telluride when forced melt convection is applied. Journal ofCrystal Growth 535, 125542. doi: .Mont´emont, G., Lux, S., Monnet, O., Stanchina, S., Verger, L., 2014. Studyingspatial resolution of czt detectors using sub-pixel positioning for spect. IEEETransactions on Nuclear Science 61, 2559–2566. doi: .Ocampo Giraldo, L., Bolotnikov, A.E., Camarda, G.S., De Geronimo, G., Fried,J., Gul, R., Hodges, D., Hossain, A., ¨Unl¨u, K., Vernon, E., Yang, G., James,R.B., 2018. Study of sub-pixel position resolution with time-correlated tran-sient signals in 3D pixelated CdZnTe detectors with varying pixel sizes.Nuclear Instruments and Methods in Physics Research A 884, 136–139.doi: .Persson, M., Pelc, N.J., 2019. Simulation model for evaluating energy-resolving photon-counting CT detectors based on generalized linear-systemsframework, in: SPIE proceedings, p. 109481V. doi: .Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T., 2007. NumericalRecipes. Cambridge University Press.Rana, V.R., Cook, Walter R., I., Harrison, F.A., Mao, P.H., Miyasaka, H., 2009.Development of focal plane detectors for the Nuclear Spectroscopic Tele-scope Array (NuSTAR) mission, in: Siegmund, O.H. (Ed.), UV, X-Ray,and Gamma-Ray Space Instrumentation for Astronomy XVI, p. 743503.doi: .Redus, R.H., Pantazis, J.A., Huber, A.C., Jordanov, V.T., Butler, J.F., Apo- ovsky, B., 1997. Fano factor determination for czt. MRS Proceedings 487,101. doi: .Ryan, D., Christe, S., Shih, A., Inglis, A.R., Gregory, K., Baumgartner, W.H.,Gaskin, J., Wilson-Hodge, C., Seller, P., Wilson, M., Veale, M.C., Panessa,M., 2016. HEXITEC: A Next Generation Hard X-ray Detector for SolarObservations, in: AAS / Solar Physics Division Abstracts .Shockley, W., 1938. Currents to Conductors Induced by a Moving PointCharge. Journal of Applied Physics 9, 635–636. doi: .Veale, M.C., Bell, S.J., Duarte, D.D., Schneider, A., Seller, P., Wilson, M.D.,Iniewski, K., 2014. Measurements of charge sharing in small pixel CdTedetectors. Nuclear Instruments and Methods in Physics Research A 767,218–226. doi: .Wahl, C.G., Kaye, W.R., Wang, W., Zhang, F., Jaworski, J.M., King, A.,Boucher, Y.A., He, Z., 2015. The Polaris-H imaging spectrometer. NuclearInstruments and Methods in Physics Research A 784, 377–381. doi: .Winkler, A., Naaranoja, T., G¨adda, A., Ott, J., Luukka, P., Karadzhinova-Ferrer,A., Kalliokoski, M., H¨ark¨onen, J., 2019. Optical and electrical characteri-zation of Cadmium Telluride X-ray pad detectors. Nuclear Instruments andMethods in Physics Research A 924, 28–32. doi: .Wohl, C.G., Cahn, R.N., Rittenberg, A., Trippe, T.G., Yost, G.P., Porter, F.C.,Hernandez, J.J., Montanet, L., Hendrick, R.E., Crawford, R.L., Roos, M.,T¨ornqvist, N.A., H¨ohler, G., Aguilar-Benitez, M., Shimada, T., Losty, M.J.,Gopal, G.P., Walck, C., Shrock, R.E., Frosch, R., Roper, L.D., Trower, W.P.,Armstrong, B. (Particle Data Group), 1984. Review of particle properties.Rev. Mod. Phys. 56, S1–S299. URL: https://link.aps.org/doi/10.1103/RevModPhys.56.S1 , doi: .Yakimov, A., Smith, D., Choi, J., Araujo, S., 2019. Growth and characterizationof detector-grade CdZnTeSe by horizontal Bridgman technique, in: SPIEproceedings, p. 111141N. doi: .Yin, Y., Chen, X., Li, C., Wu, H., Komarov, S., Guo, Q., Krawczynski, H.,Meng, L.J., Tai, Y.C., 2014. Evaluation of PET Imaging Resolution Using350 mu { m } Pixelated CZT as a VP-PET Insert Detector. IEEE Transactionson Nuclear Science 61, 154–161. doi: .Yin, Y., Chen, X., Wu, H., Komarov, S., Garson, A., Li, Q., Guo, Q., Krawczyn-ski, H., Meng, L.J., Tai, Y.C., 2013. 3-d spatial resolution of 350 / spl mu / mpitch pixelated cdznte detectors for imaging applications. IEEE Transactionson Nuclear Science 60, 9–15. doi: .Yin, Y., Chen, X., Wu, H., Komarov, S., Lee, K., Guo, Q., Krawczynski, H.,Tai, Y., 2011. Resolution improvement by interpolation of charge sharingevent position in 350 µ m pitch pixelated cdznte detectors, in: 2011 IEEENuclear Science Symposium Conference Record, pp. 3263–3266. doi: .Zhang, F., He, Z., Xu, D., 2004. Analysis of Detector Response Using 3-DPosition-Sensitive CZT Gamma-Ray Spectrometers. IEEE Transactions onNuclear Science 51, 3098–3104. doi: .Zhang, F., Herman, C., He, Z., De Geronimo, G., Vernon, E., Fried, J., 2012.Characterization of the H3D ASIC Readout System and 6.0 cm .Zhang, S., Wang, C., Zhao, B., Zhang, H., Zheng, L., 2018. Controlling Teinclusion during direct mixed solution growth of large size CdZnTe crystal,in: SPIE proceedings, p. 107620V. doi: .Zhang, W.W., Allgood, K.D., Biskach, M.P., Chan, K.W., Hlinka, M., Kearney,J.D., Mazzarella, J.R., McClelland, R.S., Numata, A., Riveros, R.E., Saha,T.T., Solly, P.M., 2018. Astronomical x-ray optics using mono-crystallinesilicon: high resolution, light weight, and low cost, in: den Herder, J.W.A.,Nikzad, S., Nakazawa, K. (Eds.), Space Telescopes and Instrumentation2018: Ultraviolet to Gamma Ray, International Society for Optics and Pho-tonics. SPIE. pp. 130 – 139. URL: https://doi.org/10.1117/12.2312879 , doi: ..