X-ray Photon Processing Detectors: Space, Industrial, and Medical applications 3031352408, 9783031352409

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Conny Hansson Krzysztof (Kris) Iniewski   Editors

X-ray Photon Processing Detectors Space, Industrial, and Medical applications

X-ray Photon Processing Detectors

Conny Hansson • Krzysztof (Kris) Iniewski Editors

X-ray Photon Processing Detectors Space, Industrial, and Medical applications

Editors Conny Hansson Stanford University SLAC National Accelerator Laboratory Menlo Park, CA, USA

Krzysztof (Kris) Iniewski Emerging Technologies CMOS Inc. Port Moody, BC, Canada

ISBN 978-3-031-35240-9 ISBN 978-3-031-35241-6 https://doi.org/10.1007/978-3-031-35241-6

(eBook)

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

Preface

Currently, most digital radiation detectors for medical and industrial applications are based on integrating the X-ray photons emitted from the X-ray tube for each frame. This technique is vulnerable to noise due to variations in the magnitude of the electric charge generated per X-ray photon. Higher energy photons deposit more charge in the detector than lower energy photons so that in a quantum integrating detector, the higher energy photons receive greater weight. This effect is undesirable in many detection applications because the higher part of the energy spectrum provides lower differential attenuation between materials, and hence, these energies yield images of low contrast. Photon counting X-ray quantum counting detectors solve the noise problem associated with photon weighting by providing better weighting of information from X-ray quanta with different energies. In an X-ray quantum counting system, all photons detected with energies above a certain predetermined threshold are assigned the same weight. Adding the energy windowing capability to the system theoretically eliminates the noise associated with photon weighting and decreases the required X-ray dosage by up to 50% compared to integrating systems. Silicon, germanium, and high-Z materials like CdTe, CZT, GaAs, and perovskites offer the best implementation possibility of direct conversion X-ray detectors. We discuss material challenges, detector operation physics and technology, and readout integrated circuits required to detect signals processes by these sensors. We will conclude providing examples of applications of photon pixel detectors in medical imaging, high energy physics, non-destructive testing, and security. Menlo Park, CA, USA Port Moody, BC, Canada

Conny Hansson Krzysztof (Kris) Iniewski

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Contents

Introduction to Detector Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conny Hansson and Krzysztof (Kris) Iniewski

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Charge Sharing in Single-Photon-Counting Detectors . . . . . . . . . . . . . . . . . . . . . . Aleksandra Krzyzanowska

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Sub-pixel Sensing for Pixelated CdZnTe Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . Yuefeng Zhu

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Machine Learning Approaches in Room Temperature Semiconductor Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Srutarshi Banerjee, Miesher Rodrigues, Manuel Ballester, Alexander Hans Vija, and Aggelos K. Katsaggelos High Energy Resolution X and Gamma Ray Imaging Spectroscopy with the ORION Multichip Readout Electronics. . . . . . . . . . . . . Filippo Mele

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MIRA: A Low-Noise Pixelated ASIC for Photon Counting Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Edoardo Fabbrica, Marco Carminati, and Carlo Fiorini Development of the Analog Front-End Circuit for the CMS Pixel Readout Chip at the HL-LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 L. Gaioni, A. Galliani, M. Manghisoni, L. Ratti, V. Re, E. Riceputi, and G. Traversi A Readout Electronic System for a 3D Position-Sensitive CdZnTe Gamma-Ray Spectrometer Based on the CPRE10-32 Readout ASIC . . . . . 155 Tianze Chen, Xiaohui Li, Ke Wang, CunFeng Wei, Lei Shuai, Xiaopan Jiang, Na Wang, Mian Wang, and Long Wei Space Applications of CdZnTe and CdTe Detector Systems: Past, Present and Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Branden Allen vii

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Contents

Germanium Detectors for MeV Gamma-Ray Astrophysics with the Compton Spectrometer and Imager . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Jacqueline Beechert, Hadar Lazar, and Albert Y. Shih Particle Measurements in Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Martin Kroupa, Jonathan Barney, August Gula, Carlos Maldonado, Thomas Campbell-Ricketts, and Stuart George Photon Counting Detectors: Applications in Radiotherapy . . . . . . . . . . . . . . . . . 269 Alex Winkler Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

About the Editors

Conny Hansson has an M.Sc. in both Space Engineering (Umea University, Sweden) and Electrical Engineering (Halmstad University, Sweden) and earned his doctorate in Material Science from the University of Manchester, United Kingdom. He has spent over 15 years engaged in the design, construction, characterization, and implementation of novel X-ray, gamma-ray, charged particle, and IR detectors for a number of different application areas including space science, particle physics, accelerator facilities, security, and medical imaging. During this time, Dr. Hansson has worked at the European Space Agency’s European Space Research and Technology Center (ESTEC), the Dutch National Institute for Subatomic Physics (NIKHEF), both in the Netherlands, and at Redlen Technologies Inc., Canada. Much of his work has been dedicated to the development of compound semiconductor sensors and dedicated Application Specific Integrated Circuits (ASIC’s), and as such he has been involved in all areas of required technical development, including sensor growth and characterization; ASIC development; prototype detector qualification; integration of detector in final instrumentation; and evaluation of instrument performance. He currently holds a Staff Engineer – Detectors and Scientific Instrumentation position at the LCLS detectors group, SLAC National Accelerator Laboratory, Stanford University, USA. Krzysztof (Kris) Iniewski is managing R&D development activities at Redlen Technologies Inc., a detector company based in British Columbia, Canada. During his 15 years at Redlen, he has managed development of highly integrated CZT detector products in medical imaging and security applications. Prior to Redlen, Kris hold various management and academic positions at PMC-Sierra, University of Alberta, SFU, UBC, and University of Toronto. Dr. Iniewski has published over 150+ research papers in international journals and conferences. He holds 25+ international patents granted in USA, Canada, France, Germany, and Japan. He wrote and edited 75+ books for Wiley, Cambridge University Press, McGraw Hill, CRC Press, and Springer. He is a frequent invited speaker and has consulted for multiple organizations internationally.

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Introduction to Detector Technologies Conny Hansson and Krzysztof (Kris) Iniewski

1 Radiation Detectors The operation of any radiation detector depends on how the radiation interacts with the sensor material of the detector. The interaction needs to cause a measurable change in the physical properties of the sensor, typically a change in the number of free carriers available to conduct current.1 Electronic circuits then measure and further process this change in sensor property to extract information about the detected photon. The subject of this chapter pertains detection of X-rays and γrays using semiconductor sensors and the associated front-end electronics. More specifically, a largely qualitative treatise on the physics and principles of hybrid and monolithic pixel detectors is given. The basic steps in detecting an X-ray photon by a semiconductor sensor are described as follows: An X-ray impinges on a semiconductor crystal and interacts with the atoms of that crystal, creating a charge cloud consisting of electrons and holes. The electron-hole clouds are accelerated in opposite directions due to the electric field applied across the sensor via the electrodes. The movement of these charge carriers is sensed at the electrode, creating a current in the amplifier

1 Although the creation of an electrical pulse is the most common method of detecting a photon, alternatives excist, such as the creation of optical photons for scintillators and heat increase (phonons) in bolomteters.

C. Hansson () Stanford University, SLAC National Accelerator Laboratory, Menlo Park, CA, USA K. (Kris) Iniewski Redlen Technologies, Saanichton, BC, Canada © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_1

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Fig. 1 Basic configuration for detection of X-rays in a semiconductor detector. The sensor and funtctional blocks making up the electronics chain is illustrated

that is measured and evaluated per what property is being determined. This basic measurement process and the associated detection chain are illustrated in Fig. 1. Depending on the sensor and the electronics design, it is possible to extrapolate different properties related to the measured photons. The most common properties of interest are the position of interaction, photon energy, and time of arrival of the photon. The position is required to get an image of the photon source. As such, detailed information regarding the photon interaction point in the sensor is required. This is achieved by segmenting, i.e., pixelating, the sensor. Energy determination is required to measure the source’s spectrum, i.e., the energy deposited by each interacting photon. This requires us to ensure the full photon energy is deposited and subsequently measured accurately. Finally, the photon arrival time can be used to perform timing measurements and evaluate how long the photon has traveled w.r.t. a set time frame (Time of Flight). We therefor need to be able to identify when the photon is absorbed in the sensor, and relate it to the external time frame of interest. This chapter is divided into a section discussing the properties of the sensor, followed by a description of the electronics.

2 Sensor and Sensor Physics The sensor is the part of the detector where the X-ray interaction takes place, and the signal that is measured by the electronics originates. Here a comprehension of the photon/sensor interaction and charge cloud generation must be obtained to understand the sensor’s behavior. Also, understanding the subsequent charge cloud transport and signal generation mechanisms is needed. The details of these processes are discussed in the following sections, starting with the photon/sensor interaction mechanisms present in semiconductor sensors.

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2.1 X-Ray and Gamma-Ray Interactions with Sensors When X-rays enter a semiconductor sensor, it has a finite probability to be absorbed. An X-ray beam entering a sensor will be attenuated according to: .

I = e−μa ρx I0

where I is the intensity of the X-ray beam after it has traveled a distance x into the material, I0 is the beam’s intensity prior to entering the sensor, ρ is the mass density of the material, and μa is the attenuation coefficient of the material. The attenuation coefficient of the material is given by adding the attenuation coefficients of each of the x-ray matter interactions that can take place in that sensor. X-rays and γrays interact with matter mainly by four basic processes: photoelectric absorption, elastic scattering, Compton scattering, and pair production. In photoelectric absorption [1], all the photon’s energy is transferred to an atomic electron, with the highest probability electron being a K-shell electron. The electron that receives the energy from the photon, referred to as a photoelectron, becomes free to move in the sensor and interacts with neighboring atoms creating a charge cloud [2]. The atom that gave up the photoelectron ends up in an excited state. Usually, the excited atom is relaxed by having a higher orbital electron fill the vacancy, emitting a characteristic photon in the process. Under normal conditions, the characteristic photon is reabsorbed in the sensor, creating a second charge cloud that is measured together with the original charge cloud. For a given X-ray photon energy, E, the total number of charge carriers, N, in the charge cloud is given by: N=

.

E W

where W is the material dependant pair creation energy, which dictates the energy it takes to create an electron-hole pair. However, if the characteristic electron can travel far enough to leave the sensor, only part of the total photon energy will be measured. When reconstructing photon spectra, these partial depositions, referred to as escape peaks, can sometimes be seen as additional energy lines located below the main peak, with an energy difference corresponding to the energy of the characteristic photon. Both Rayleigh [3] and Thomson scattering fall under the category of inelastic scattering. In this process, the photons interact with the sensor’s atoms but do not impart any energy. Instead, the photons are just redirected at an angle with respect to their incoming trajectory. As such, it does not create a charge cloud and is not detected by the detector electronics.

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In Compton scattering [4], also known as elastic scattering, the photon will impart some of its energy to a loosely bound electron, known as a recoil electron, and then be scattered at an angle. The amount of energy that is imparted to the recoil ◦ electron depends on the photon scattering angle. At 0 no energy is transferred to the ◦ electron, and the maximum energy transfer occurs at180 . As no energy larger than this maximum energy can be deposited, it creates an upper energy limit referred to as the Compton edge. Finally, pair production can occur if the photon has an energy exceeding 1.022 MeV. This process takes place in the columb field of an atomic nucleus, and the photon is transformed into an electron-positon pair. Any energy exceeding 1.022 MeV will be imparted as kinetic energy for the newly created pair. After slowing down, the positron annihilates, creating two annihilation photons. For the described interaction mechanisms, only photoelectric absorption results in the whole photon energy being deposited in the sensor. As such, especially for spectroscopic detectors, it is preferential to try and ensure this is the most probable interaction mechanism. In Fig. 2 we can see the regions where the different interaction mechanisms dominate as a function of the sensor’s atomic number, Z, and the photon energy. From the graph, it is clear that decreasing the photon energy and/or increasing the atomic number of the sensor increase the probability of photoelectric absorption being the dominant interaction mechanism. A more detailed view of the relative probability of the different interaction mechanisms for Si can be seen in Fig. 3. This plot shows that the photoelectric effect is dominant at lower energies and remains the primary interaction mechanism across the entire range. Compton only starts to have a noticeable impact on the absorption in the sensor when the photon energy reach 60–70 keV.

Fig. 2 Illustration of where in phase space the three interaction mechanisms between matter and sensor are dominant, as a function of the atomic number of the sensor and energy of the photon. The atomic number for Si, GaAs, Ge, and CdZnTe are highlighted. (Reproduced from Ref. [5])

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Fig. 3 Relative efficiency of interaction mechanisms for Silicon as a function of photon energy. As seen from the graph, Compton scattering only start to play a significant role around 60 keV. Attenuation coefficients used to produce the plot was taken from [6]

2.2 Sensor Detection Efficiency As discussed, the atomic number of the sensor plays a significant role in the detection efficiency of the sensor,2 as do the sensor thickness and the structure of the entrance window.3 The effect of atomic number can be seen in Fig. 4, where the detection efficiency at different photon energies are seen for different sensor materials. For ease of comparison the absorption efficiency for all materials are shown for a sensor thickness of 500 um. It should be noted that these plots assume no entrance window at all. It is seen from the plot that a higher detection efficiency is achieved with a higher atomic number material sensors. However, the absorption edges of the materials also have to be considered for different energy regions. This is seen for CdZnTe in the 27 keV region where the absorption edges result in the sensor having a worse detection efficiency than what is observed for Ge and GaAs.4 The effect of the sensor thickness is seen in Fig. 5, where the detection efficiency is plotted for Si sensors with two different thicknesses. While this has no effect in the lower energy regions, a clear increase is apparent at the higher end. While these plots show the effect of the atomic number and thickness of a sensor, they are plotted without considering the entrance window’s effect.

2 Here the term detection efficiency refers to the ratio of the number of detected photons vs the total number incoming photons. Other definitions do exist that take into account the detector response function. 3 The entrance window is somethimes called the deadlayer, and referes to any layers or structures on the entrance side of the sensor that do not create a measureable signal for the photons that are absorbed within it. 4 Due to the similar atomic number and density of Ge and GaAs the lines for these materials ovelap eachother in the plots in Fig. 4.

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Fig. 4 Detection efficiencies as a function of photon energy for different sensor types. The efficiency has been plotted for a 500 μm sensor of each material type, and photon absorption in the entrance window is neglected

Fig. 5 Detection efficiency as a function of photon energy for two different thicknesses of Si. The photon absorption in the entrance window is neglected

For the case of resistive devices, such as CdTe, GaAs, and CdZnTe, the primary consideration for the entrance window is the metal contacts used to establish an electric field across the sensor, attached to both sides of the sensor. For a junction device, such as Si sensors, a small region of non-sensitive Si created at the pnjunction region and a thin layer of Al, used to block visible light, usually constitutes the entrance window. For both resitive and junction devices, the effect of the entrance window is to reduce the detection efficiency at the lower photon energy end of the spectra. The effect is illustrated in Fig. 6, where the detection efficiency

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Fig. 6 Detection efficiency as a function of photon energy for a 500 um thick Si sensor. The effect of taking the entrance window into account is illustrated. For these calculations, an entrance window consisting of a 1 um thick non-responsive Si region and a 1 um thick Al layer (optical light shield) have been used

is compared for a sensor with just 500 μm Si with and without an entrance window. The entrance window used here consitited of a 1 μm Al layer and a 1 μm insensitive silicon region. The plot clearly shows the need to carefully consider, and optimize, the entrance window when designing X-ray detectors targeted at low X-ray energies [7, 8].

2.3 Photon Absorption Profiles in Sensors While the detection efficiency curves seen in the previous section give a good insight into the probability that the sensor detects a photon at any one photon energy, the absorption profile for the sensor also plays an essential role in understanding and designing the operation of a sensor. As discussed in the section on sensor geometry, for certain sensor geometires which charge carrier type is responsible for the charge induction onto the readout electronics depends on where in the sensor that charge is present. Also, it is common to use oxide layers for insulation in the pixel electrode area for various reasons. As oxides are prone to radiation damage,5 it is sometimes a requirement that photons cannot reach this far into the sensor. The X-ray absorption profiles in a semiconductor sensor follow an exponentially falling function, as shown in Fig. 7. As the photons will be absorbed through photoelectric absorption, their energy will be entirely deposited in a single interaction point. Therefore, the graphs in Fig. 7 can be interpreted as the probability of a 5 As carriers that are excited by X-ray photons in insulators are not free to move, they are unable to recombine or escae the region, leading to a gradual charging of the oxcide, which can effect the electrical potential of the region, leading to unwabted behavior or outright failure of the device.

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Fig. 7 X-ray photon absorption profiles for various sensor materials, photon energies, and sensor thicknesses. (a) The absorption profiles for various materials for 16 keV photons, showing the impact of using different sensor material. (b) The variation in absorption profiles of 16keV photons and 8 keV photons, showing the impact of the photon energy on a set material system. It should be noted that for X-ray interactions, this profile corresponds to the probability of a photon being absorbed at a specific depth in the sensor. This is in contrast to the absorption profiles plotted for charge particles, where the amount of charge deposited as a function of depth traveled for a particle into the sensor is usually visualized

photon being absorbed at a specific depth in the sensor.6 The absorption profile for a sensor is strongly dependent on the sensor’s atomic number and the energy of the incoming photon. The effect of the atomic number can be seen in Fig. 7a, where the absorption profile for 16 keV photons has been plotted for 500 μm thick sensors of different materials. The probability of being absorbed close to the entrance window increases with increassing atomic number of the sensor. As such, a much steeper function for a higher atomic number sensor is observed. While CdZnTe has a higher average atomic number than either GaAs or Ge, the absorption profile for CdZnTe at 16 keV is less steep then for these materials. This is due to the influence of one of the absorption edges of CdZnTe reducing the absorption probability in this part of energy space. Going to energies above the edge sees the CdZnTe sensor recovering its absorption capability. This illustrates the need to consider absorption edges for various sensors when understanding the response for a specific energy range. The effect on the absorption profile with photon energy is illustrated in Fig. 7b, where the response can be seen for 8 and 16 keV in a 500 μm thick Si sensor. A much steeper curve is observed at 8 keV with a higher absorption probability close to the entrance window. It should also be noted that we have full detection efficiency at this energy, as indicated at 8 keV for Si in Fig. 6. However, the absorption profile becomes much more level when the photon energy increases to 16 keV. Also, many photons make it through the sensor at this energy without being detected. This can

6 In contracts to the absorption profile for a charged particle, where the charge pf the particle is gradually deposited along its path, and the profile corresponds to the amount of charge that is deposited at any a specific depth in the detector.

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be seen by the absorption probability not being zero at the back end of the sensor and that detection efficiency has fallen from 100% to 63%.

2.4 Basic Sensor Configurations – Resistive Device and PN-Junction Device Once a charge cloud has been created by the photon we need to be able to measure the pulse these carriers create. The be able to do so, the resistivity, ρ, of the sensor material is key. The resistivity of a material is set by the number of free carriers and the ability of those carriers to move under the influence of an electric field. This is mathematically expressed in the equation below [9]: ρ=

.

1 ne (μe + μh )

where n is the number of free carriers, e is the charge of an electron and μe and μh are the electron and hole mobility, respectively. In a semiconductor, the amount of free carriers can be set by either the number of carriers that have been able to be thermally excited across the bandgap, the amount of doping, and/or the amount of carriers that have been released/captures from various trapping states.7 The resistivity for several common detector materials can be seen in Table 2. The material’s resistivity is a crucial parameter for sensor materials as it dictates the amount of leakage current in the sensor. The leakage current is the amount of current flowing without any photons incident of the device (also referred to as dark current). As the leakage increase, so does the statistical variation of that current, which manifests as noise in a measurement. As such, the leakage current has to be low enough for the electronics to be able to handle it and for the induced current caused by the photon created charge cloud to be distinguishable from the leackage noise [10]. Some of the materials stated in Table 2, namely CdZnTe, GaAs, and TlBr, have resistivities that allow the X-ray photon-generated signals to be detected with only mild cooling. These materials can be operated by attaching electrodes directly on opposite sides of the crystals and applying an electric field between the electrodes. If the sensor is operated in this way, it is said to be a resistive sensor. However, for some of the materials in Table 2, i.e., Si and Ge, the amount of leakage would

7 If the electrical property of the material is dictated by carriers that have been thermally excited across the bandgap, the material is said the be intrinsic, while if the amount of doping sets the number of free carriers available to carry current, the material is said the be extrinsic. If a significant number of defects or impurities are also present, they can contribute to the number of free carriers either by adding additional carriers or acting as trapping sites that captures carriers and prevent them from moving. Additionally, these trapping sites can alter the mobility of the carriers and, if in sufficient density, result in locally charged region resulting in electric field distortions (i.e. polarization effects).

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Fig. 8 Basic configurations for a resistive sensor, (a), and a pn-junction sensor, (b). For the resistive sensor, metal electrodes are deposited on either side of the sensor, and an electric field is applied between the two. For the pn-juntion sensor, doping is used to create a junction and a corresponding depletion region. As the bias across the junction increases, the depletion region starts to grow. In this type of sensor, only the depleted part of the sensor is fully responsive to photon interactions, and the maximum achievable depletion width often limits the maximum sensor thickness. The use of a depletion region in a pn-juntion sensor is introduced to get rid of the excess carriers in the material bulk. In contrast, the carrier concentration is low for the resistive sensor to detect photons without a depletion region

be prohibitive to operate as a resistive device, and they are operated as depletion devices instead. This is usually done by creating a pn-junction on one side of the sensor that is then reverse-biased to have the resulting depletion region, i.e., the region where free carriers have been removed, extend throughout the sensor volume. This effectively reduces the leakage of the material to the point where the signal can be detected. These types of sensors are often referred to as junction or diode sensors. The two types of configurations can be seen in Fig. 8. It should be noted that while for the resistive device, the bias applied results in an electric field across the entire device, similar to what would be expected for a plate capacitor,8 for the junction device, this is not necessarily the case. As a bias is applied to the pn-junction the depletion region will start to grow from the pimplant side towards the backside with increased bias voltage. Since the depleted region of the sensor will have a much higher resistivity then the non-depleted region, the electric field will primarily be established across this section, As such, the electron-hole clouds created by a photon absorbed in the non-depleted region will not experience any electric field. Consequently, the charge clouds will not separate and the carriers recombine, effectively ensuring the detector electronics do not detect the photon.9 As such, it is critical when operating a pn-junction sensor to ensure the sensor is biased high enough to fully deplete and make the entire sensor

8 It

should be noted that this assumes that both metal contacts create ohmic contacts with the semiconductor. 9 The charge cloud created in this region will still diffuse and some of the charge will make it to the depleted region and be detected. However, this will result in a much lower charge and is neglected

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Fig. 9 The electric field line profiles for planar and pixelated devices can be seen in (a) and (b), respectively. In addition, a 1D cross-section of the weighting field for both detectors is illustrated in (c), clearly showing the effect on the weighting field caused by pixelating the electrode (electrode to thickness ratio: 0.125). The location of the cross sections is indicated by the red dashed lines in (a) and (b)

area sensitive to photons.10 For a more in-depth discussion on various detector configurations the reader is directed to [9, 10].

2.5 Sensor Geometry – Planar and Pixel Detectors In order to ensure the electrons and holes that consititute the charge cloud separate and induce a signal on the electronics, and electric field has to be established between the sensor electrodes. The most straightforward electrode configuration for a semiconductor sensor can be seen in Fig. 9a. This configuration is refered to a a planar configuration and consists of two large electrodes deposited on opposite sides of the sensor. As a result, the electric field resulting from biasing the electrodes creates a uniform electric field across the sensor’s active area, as indicated by the dashed blue electric field lines. While this configuration is the technically easiest to realize, a photon can interact anywhere in the sensor volume, and no finer information regarding the interaction location can be obtained, i.e., the detector does not have any spatial resolution outside of the size of the detector itself. If the detector’s targeted application requires spatial resolution, such as is the case for example in imaging, a more complicated electrode configuration is needed. This can be realized by segmenting one of the electrodes into sections, effectively creating a pixelated device, and having each pixelated electrode read out by an electronic channel. This is illustrated in Fig. 9b.

in the description to clarify the effect that not having a fully depleted device will have on the sensor performance. 10 It should be noted here that not fully depleting the device will make the sensor have worse low photon energy response since they will be preferentially absorbed in this non-depleted region. This is sometime referred to as the entrance window and is of key importance to minimize for low energy X-ray detectors (usually of concern in the 1010 1.51 + 0.606x + 0.139x2 4.6 1350

TlBr 81,35 7.45 1012 2.68 6.5 50

480

1900

400

120

4

>1 ~1

>1 >1

1 × 10−4 4 × 10−6

1 × 10−2 2 × 10−4

3 × 10−4 6 × 10−5

semiconductors Si and Ge are considered the gold standard for sensor materials. This is primarily due to the extremely high-quality crystals available for these materials. As such, they have excellent transport properties and do not suffer from any polarization effects.18 However, they suffer from some limitations, leading to an interest in alternative materials systems. The primary drawback of Si is its low atomic number, which prevents it from having a high detection efficiency at higher X-ray energies. This drawback in Si has been the primary driver behind the development of high-Z semiconductor materials, namely GaAs, CdTe, CdZnTe, and TlBr, for X-ray sensors. While Ge has a reasonably high atomic number, this material also has a very small bandgap. This results in Ge having better intrinsic energy resolution than Si, but it also leads to the need to cool this material, often to cryogenic temperatures, to reduce the thermally generated leakage current and be able to differentiate a photon signal. The need for such significant cooling forces the use of vacuum operation and bulky cooling equipment to operate these detectors. While this can be dealt with for specific applications, it becomes preventative for others, such as space-based applications. As can be seen from Table 2, GaAs offers an alternative to Ge with very similar atomic number and density values but with a much wider bandgap, effectively reducing the need for cooling. The larger bandgap also ensures that GaAs have similar carrier concentrations to depleted Si, meaning it can be operated as ‘depleted’ without pn-junctions [10, 16]. Additionally, GaAs have excellent carrier mobilities, which has led to it being identified as a material of interest for sensor materials that require swift pulse response (fast timing application) [17]. However, the promising features promised by GaAs are currently being prevented by the material quality, with a large number of impurity states present [18, 19]. This leads to reduced transport properties, as seen from

18 Here

the term polarization effect is used to indicate any time dependent change in detector performance when all other parameters are kept constant.

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this material’s very low mobility-lifetime products. Additionally, deep-level traps19 resulting in regional distortions of the electric field have been observed [20]. These problems plaguing GaAs have limited its use to thin sensors, reducing the detection efficiency at higher photon energies. TlBr is available from a few select companies for use as X-ray sensors. However, material quality issues, low hardness, and its nature as a mixed electric-ionic conductor has so far prevented it from being used in commercial products [17]. The most developed high Z sensors currently available are CdTe and CdZnTe. While suffering from material quality issues, they have reached a maturity level that has allowed them to be used in commercial products. While some producers have managed to produce CdZnTe allowing for stable operation even under very high flux conditions, CdTe is still suffer from polarization effects [21, 22].20 For a more detailed coverage of various detector materials and their properties the reader is directed to [17].

3 Detector Electronics The charge pulse that is generated in the sensor is induced on the electronics, where it is then processed according to the photon parameter of interest. Two common architectures for electronics design are the pulse processing design, also referred to as the photon counting design, and the charge integrating design [23]. The basic operation of these designs is dictated by the reset methodology used by the first stage in the electronic chain, the Charge Sensitive Amplifier (CSA). The following sections discuss the differences between these two architectures and what pulse parameter is used to determine the most common photon parameters of interest. Finally, the implementation of these electronic designs into the two Application Specific Integrating Circuit (ASIC) solutions, the hybrid pixel detector design and the monolithic pixel detector design, is discussed.

3.1 Pulse Processing and Charge Integrating Electronics Many different amplifier solutions exist to measure the signal generated by detecting an X-ray photon in a semiconductor sensor, including current and voltage amplifiers. However, one of the most used ones is the charge-sensitive amplifier (CSA) [13, 16]. The primary reason for the popularity of the CSA is the fact that the gain remains the same regardless of the capacitive loading on its input that the sensor subjects it to, a fact that is not true for many other amplifier solutions.

19 The

EL2+ mid gap defect caused by As substitutionally occupying a Ga lattice site. CdTe polarization is strongly linked to operation with schottky contatcs that are used to reduce the amount of leackage current from this material. 20 For

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Fig. 10 Illustration of a basic sensor/csa/filter network used for X-ray detection. As the charge cloud that the X-ray photon has created starts to move, a signal is induced onto the CSA. A filter is often used at the output of the CSA to limit the bandwidth of the newtwork and reduce the system noise. A trade-off between increased noise performance (low bandwidth) and pulse response time (high bandwidth) often has to be done to optimize for the application. In the system above, no reset mechanism is present

The basic operation of the CSA can be seen in Fig. 10. Once the X-ray photon creates charge clouds in the sensor, and these charge clouds start moving to create a current in the sensor, the charge is induced onto the feedback capacitor of the preamplifier. As this happens, the signal goes from being a current signal to a voltage signal, and as more charge is induced onto the CSA feedback capacitor, the voltage at the output of the CSA is driven up. When the full signal has been induced on the CSA, the magnitude of the voltage at the output of the amplifier is directly related to the amount of charge released by the absorbed X-ray photon. In general, the CSA is designed with a filter attached to its output. The main aim of the filter is to modify the frequency range (bandwidth) of the CSA and filter network to a more suitable one than what is given by the frequency response provided by the CSA alone. As the bandwidth of the frequency response of the CSA/Filter network is reduced, the noise is also reduced since signals not belonging to the photon-generated pulse are rejected.21 However, the bandwidth reduction also results in the rise time at the output of the CSA/Filter network becoming slower in the temporal domain (i.e., signal rise time is increased). As such, the detector needs longer to measure the signal, effectively reducing the maximum count rate the detector can handle accurately. This trade-off between noise level and countrate capability for a detector is one of the design criteria the electronics designer has to take into consideration and can serve as a general example of why a generic electronic channel for all applications can not be created, but each application has to have its dedicated solution depending on what is the most critical design 21 This is a simplistic argument highlighting a general rule that reducing the bandwidth reduces the noise. In reality a detailed study between liear, parallel and shot noise components in the systems has to be evaluated and an optimim noise performance occur at a specific shaping time (bandwidth). For a more detailed description, please see [13].

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Fig. 11 The effect of implementing a continuous reset mechanism by connecting a resistive element in parallel to the CSA feedback capacitor is illustrated. Once the charge has been fully induced onto the feedback capacitor, the resistor provides a discharge path. This results in the pulse shape seen at the far right. Care to the sensor pulse rise time, and the discharge characteristics must be taken to ensure the full charge is allowed to be developed at the CSA output

criteria for that application. How the voltage at the output of the CSA/Filter network behaves as a function of time can be seen on the furthest right of Fig. 10. Before the photon is absorbed, the output is at the baseline value. As the charge clouds are created and move through the sensor, the output voltage rises and stops at a voltage corresponding to the induced charge when the charge clouds reach the electrodes. At this point, the output stays at this voltage, and the value corresponds to the energy of the photon. If a second photon is absorbed at this point, the output will increase again. Eventually, the output of the CSA would saturate when the output reached the supply voltage (i.e., the amplifier would hit the rails). To prevent this, a reset mechanism is designed and put in parallel to the CSA feedback capacitor. Historically this function has been handled by what is known as a continuous reset solution and is what is used in photon counting detector designs. More recently, for reasons that will further elaborate on below, switched reset solutions have started to be used used in charge integrating detector designs for specific applications [23].22 Illustrations of these two reset mechanisms, and their pulse responses, can be seen in Figs. 11 and 13. For the continuous reset scheme, a resistive element is connected in parallel to the feedback capacitor. As such, once the charge has been induced on the feedback capacitor it has a path to discharge. The resulting pulse shape can be seen at the furthest right in Fig. 11. Once the charge has been induced, it starts to discharge

22 Continuous reset and switched reset are also sometimes referred to as time-independent reset and time dependant reset respectively. This is due to their general nature where the continuous reset will respond to the incoming charge as it comes in, and therefore always have the same response, while for the switched reset happens at a set time, and the response to a photon can vary depending on when in time (w.r.t. the photon arrval time) the pulse characteristic measurement takes place.

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Fig. 12 Common pulse characteristics that can be measured to establish specific photon characteristics in a continuous reset system

towards the baseline value (i.e., reset), and a pseudo-Gaussian pulse shape is created where the pulse’s height corresponds to the photon’s energy. For the rising edge of the pulse, care must be taken to ensure that the signal has enough time to develop before the discharge starts taking effect. Otherwise, the full pulse height might not present, an effect referred to as ballistic deficit. For the pulse’s falling edge, consideration must be taken so that the signal returns to the baseline fast enough before the next pulse comes in (i.e., the reset time has to be commensurate with the expected count rate). If this does not happen the pulse of the second event will be superimposed on the tail of the first pulse, an effect referred to as pulse pile-up or simply pile-up. While measuring the pulse height to establish the amount of energy deposited by the X-ray photon was used above to describe the operation of this type of reset scheme, it is not the only feature of the pulse that can be evaluated, as is illustrated in Fig. 12. If a threshold circuit is added to the output of the filter, an electronic threshold can be used to evaluate if the pulse is above a specific voltage value. If it is, three additional parameters can be measured: the Time of Arrival (ToA), Time over Threshold (ToT), and counting. For the ToA measurement, the exact time when the pulse goes above the threshold is measured with respect to a reference timing. As such, the photon’s arrival time can be determined, and the detector can be used for timing measurement applications. If the transition across the electronic threshold is coupled to a counter, the circuitry can also be used to measure the number of photons (counting). Finally, by measuring the amount of time the signal stays above the threshold, again w.r.t. a reference timing, a second way to measure the photon’s energy can be achieved. As mentioned above, this reset scheme has historically been the most used. However, with the new generation of X-ray sources, i.e., next-generation synchrotron sources and X-ray free electron lasers, the time between photons arriving is

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Fig. 13 The effect of using a switched reset scheme is illustrated. For this system, the output of the filter is measured before and after the X-ray pulse has been allowed to develop. The difference gives the amount of energy deposited by the photons and is usually measured using a CDS circuit (not shown). For this reset scheme, the timing of the incoming x-rays and the readout of the electronics has to be synchronized. Also, since the reset mechanism consists of a switch incorporated in the amplifier’s feedback loop, the circuit has to be given time to stabilize after switching occurs or much noise is introduced in the measurement

becoming so short that it is not possible for the electronics to reset between events. For example, for current pixelated detectors at the LCLS X-ray free electron laser, the detectors have been designed to handle X-ray pulses arriving with up to 80,000, 8 keV, photons within a pulse width of 10 fs. As such, this type of detector has been designed to have a switched reset scheme operating as a charge-integrating detector. A switched reset scheme is realized by adding a switch in parallel with the feedback capacitor of the CSA, as can be seen in Fig. 13. the scheme works by having the switch disconnected when the photons arrive and are deposited in the sensor. The charge created by the photons is then induced onto the feedback capacitor, and the voltage at the output of the CSA/Filter network rises accordingly. After the full charge has been induced, the reset is activated by connecting the switch, creating a path for the feedback resistor to discharge. The measurement of the charge (i.e., the number of keV of photons that have been deposited in the sensor) is done by adding a correlated double sampling (CDS) circuit. This circuit first measures the baseline at the output of the filter prior to the X-ray pulse arriving (first red dot in the signal graph at the right in Fig. 13). Subsequently the final voltage at the output of the filter after the full signal has been developed is measured (second red dot in Fig. 13). Finally, the difference between these two measured values, which correspond to the total amount of photon energy, is outputted. Since the channel is not reset between the arrival of separate photons, this reset scheme cannot unambiguously determine each photon’s energy and is considered a charge-integrating detector design. Additionally, this detector design primarily works for pulsed sources since the first CDS sample has to happen after the circuit has had time to recover from

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the switch disconnecting23 (i.e. coming out of reset) and before the X-ray pulse has arrived, while the second sample has to be taken after the signal has had a chance to develop fully and before the reset happens. As such, this scheme requires the X-ray pulse and the detector’s operation to be timed together, and the X-ray pulse must arrive at a known time in the readout cycle of the detector.

3.2 Monolithic and Hybrid Pixel Detectors Many modern pixelated X-ray detectors are implemented using chips from largescale Si foundries. These chips are often referred to as Application Specific Integrated Circuits (ASIC) due to their application-tailored nature. Two groupings of these detectors that adhere to the physical principles described above are the hybrid pixel detector [24] and the monolithic pixel detector [25]. The primary difference between the two types of detectors is that the sensor and the chip containing the readout electronics are two different entities for the hybrid pixel detector. In contrast, for a monolithic pixel detector, the sensor and electronics are implemented in the same piece of Silicon. While the hybrid pixel detector technology is relatively mature, having been around for several decades, the monolithic pixel detector group is still comparatively early in its development path. As will be elucidated below, both approaches offer advantages with respect to the other. A cross-section of a pixel in a hybrid pixel detector can be seen in Fig. 14. For this type of detector, the ASIC is designed in a selected Silicon technology node and is created so that an array of readout channels are located in an array pattern that can then be coupled via bump bonding to the corresponding pixel of the sensor chip, connecting the two. The electronic chip design also typically contains signal digitization (ADC), timing circuitry, and facilities to send the chip data to the associated electronics board. This additional circuitry is sometimes referred to as the pherifial curcitry as it is commonly designed away from the chip’s central region that contains the pixel electronics channels. The main advantage of this technology is that the sensor chip and the electronics chip do not have to be created in the same technology or the same material. This last point is crucial for many applications that require high detection efficiencies at higher X-ray photon energies. Due to the low atomic number of its constituting atoms, Silicon sensors have fairly low detection efficiencies at photon energies exceeding ~20 keV. This problem can, to some degree, be alleviated by using high-resistivity Si sensors that can be depleted further into the bulk of the semiconductor. As such, the sensor can be thicker, effectively increasing the

23 Since the design of the reset scheme effectively uses a switch in the feedback loop of an amplifier, a significant amount of noise (i.e. ringing) occurs when the switch is connected and disconnected, which has to have time to settle before sampling the output of the channel can be done. If the circuit is not given enough time to recover from the switch, then the ringing is effectively sampled resulting in a very noisy signal being measured.

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Fig. 14 Illustration of the cross-section for a hybrid pixel detector. In this type of the detector, the sensor pixel and the electronic channel is connected via bump bonding. The strength of this solution is the ability to optimize the sensor and the electronics separately

detection efficiency.24 However, this solution offers relatively little reprieve as we go to even higher energies. For operation at these energies, the hybrid pixel detector trait of having the sensor and the electronic chip being different comes into its own, as it then allows for the sensor to be created in a material other than Silicon, such as CdZnTe, GaAs, or Ge. The larger atomic number of these sensors’ atomic constituents allows for a much better detection efficiency at higher energies. Detectors utilizing these high atomic number sensor materials have started to see commercial use in recent years. While the higher atomic number of these sensors offers better detection efficiencies, they are often much less developed than Si. As a result, they often suffer from drawbacks such as polarization effects, non-ideal processing methodologies, lack of doping atoms, and suitable passivation and contact materials. One also has to consider the difference in thermal expansion when using two different materials, both during detector manufacturing and during operation, if the operation occurs under a significantly different temperature than the one used for bump bonding. In the monolithic pixel detector, the sensor and electronics are created on the same die, simplifying the process as no additional high-density interconnects (i.e. bump bonding) are needed. The cross-section of a pixel from a monolithic pixel detector can be seen in Fig. 15 [25]. For this setup, the sensor part consists of the

24 While

standard Si sensors can be found with 300–500um thicknesses, high resistivity sensors with thicknesses of up to 1 mm are commercially available.

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Fig. 15 Illustration of the cross-section of a monolithic pixel detector. In this design the sensor and electroncs is designed in the same Si die. This allows for the full detector to be implemented in one process. As such, no high-density interconnect technology is needed, and since the bump bond capacitance is not present, lower noise performance can be achieved. (Reproduced from Ref. [25])

chip substrate, which is fully depleted by the backside bias. The active circuitry is located in the n and p wells (NW and PW), and additional deep wells (DPW and DNW) are incorporated to isolate the electronics from the substrate as well as act as the charge collecting electrode (DNW). In the design referenced in the figure, the pixel’s circuitry includes the CSA, filter, and CDS.25 Since the sensor and the readout electronics are created on the same die, this approach is limited to Si as the sensor material, which excludes specific high-energy applications for this technology. However, since the sensing electrode and the sensor are in the same die, no high-density interconnection is required, significantly reducing the complexity. Additionally, since there is no need for a bump bond between the CSA and the sensor, the input capacitance is significantly lowered, reducing the noise. This solution is a good option when very low X-ray energies need to be detected (>2–4 keV), as these detectors require extremely low noise to differentiate the small signal from that noise.26

25 The

line between fully monolithic detectors and semi-monolithic detectors are not completely clear currently. The detector used for the description in this section contain the sensor and the FE (CSA,filter,CDS), but does not contain the needed ADC’s and FIFO electronics. This will be provided by bonding the detector to a second chip using low density interconnects which contain this functionality [25]. As such, the detector is actually semi-monolithic detector, but for the case of simplicity this has not been elaborated on in the text. For more details on the nuances and different types of monolithic detectors under development [16] is recommended. 26 An alternative solution to the noise problem is to increase the magnitude of the photon signal. This approach is also being persued by certain groups through the use of low gain avalanche (LGAD) sensors.

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References 1. Einstein, A. (1905). Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annal der Physik, 17, 132–148. 2. Schlesinger, T. E., et al. (2001). Cadmium zinc telluride and its use as a nuclear radiation detector material. Materials Science and Engineering, 32, 102–189. 3. Rayleigh, L. (1871). Philosophical Magazine, 17, 274–447. 4. Compton, A. H. (1923). A quantum theory of the scattering of X-rays by light elements. Physics Review, 21, 483–502. 5. Decher, R., et al. (1994). X-ray and gamma ray astronomy detectors, section 1c (Library of Congress Catalogue Number 94-92211). National Aeronautics and Space Administration (NASA) Scienti_c and Technical Information Program. 6. NIST XCOM: https://physics.nist.gov/PhysRefData/Xcom/html/xcom1.html 7. Segal, J., et al. (2021). Thin-entrance window process for soft x-ray sensors. Frontiers of Physics, 9, 618390. 8. Zhang, J., et al. (2022). Development of LGAD sesnors with a thin entrance window for soft X-ray detection. Journal of Instrumentation, 17, C11011. 9. Sze, S. M., & Lee, M. K. (2012). Semiconductor devices: Physics and technology (3rd ed.). Wiley. 10. McGregor, D. S., & Shultis, J. K. (2021). Radiation detection conecpts, methods, and devices. CRC Press. 11. He, Z. (2001). Review of the Schockley-Ramo theorem and its application in demiconductor gamma-ray detectors. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 463, 250–267. 12. Owens, A., & Kozorezov, A. G. (2006). Single carrier sensing techniques in compound semiconductor detectors. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 563, 31–36. 13. Spieler, H. (2005). Semiconductor Detector Systems. Oxford University Press. 14. Veale, M. C., et al. (2014). Measurements of charge sharing in small pixel CdTe detectors. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 767, 218–226. 15. Khalil, M., et al. (2018). Subpixel resolution in CdTe Timepix3 pixel detectors. Journal of Synchrotron Radiation, 25, 1650–1657. 16. Rossi, L., Fischer, P., Rohe, T., & Wermes, N. (2006). Pixel Detectors from fundamentals to applications. Springer. 17. Owens, A. (2020). Semiconductor radiation detectors. CRC Press. 18. Greiffenberg, D., et al. (2021). Characterization of Chromium Compensated GaAs sensors with the charge-integrating Jungfrau readout chip by means of a highly collimated pencil beam. Sensors, 21(4), 1550. 19. Wheater, R. M., et al. (2021). X-ray microbeam characterisationof crystalline defects in small pixel GaAs:Cr detectors. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 999, 165207. 20. Blakemore, J. S. (1987). Gallium arsenide. American Institute of Physics. 21. Veale, M. C., et al. (2019). Cadmium zink telluride pixel detectors for high-intensity x-ray imaging at free electron lasers. Journal of Physics D: Applied Physics, 52, 085106. 22. Cola, A., & Farella, I. (2009). The polarization mechanism in CdTe Schottky detectors. Applied Physics Letters, 94, 102113. 23. Jaeschke, E. J., et al. (2020). Synchrotron light sources and free-electron lasers (2nd ed.). Springer-Verlag. 24. Ballabringa, R. (2016). Review of hybrid pixel detector readout ASICs for spectroscopic imaging. Journal of Instrumentation, 11, P01007. 25. Rota, L. (2019). Design of ePixM, a fully-depleted monolithic CMOS active pixel sensor for soft X-ray experiements at LCLS-II. Journal of Instrumentation, 14, C12014.

Charge Sharing in Single-Photon-Counting Detectors Aleksandra Krzyzanowska

1 Introduction Semiconductor pixelated position sensitive sensors are widely used in imaging and spectroscopic applications. The integration of analog and digital structures and CMOS-technology-scaling made implementation of detectors with pixel sizes even down to tens of micrometers possible. A hybrid pixel detector consists of a pixelated sensor connected electrically and mechanically via bump-bonding to an array of electronic readout channels. When an X-ray photon interacts with a detector, it deposits energy in a sensor volume. Electron-hole pairs are created in the sensor, and the charge carriers drift towards the electrodes as a result of a bias voltage applied. Detectors can be divided into those working in the integrating and single photon counting modes. In the integrating systems, signals induced by the incoming photons are integrated over a given time exposure, amplified, and digitised. However, this mode of operation, proposed to deal with high intensity of photon flux, has a limited dynamic range and a low signal-to-noise ratio because of integration of the noise. In the single-photon-counting (SPC) systems the photons are processed one by one, and in general, both the photon energy and the interaction position can be measured. Such a solution offers noise reduction, high dynamic range, and enhanced spatial resolution. However, SPC systems face limitations in operation under highflux conditions. The answer to this problem is, on the one hand, optimisation of the readout channel processing speed and, on the other hand, minimisation of the pixel size, which allows a detector to accept more photons per unit area.

A. Krzyzanowska () AGH University of Science and Technology, Krakow, Poland e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_2

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However, when the pixel sizes become smaller, the charge sharing phenomenon starts playing an important role. While charge clouds drift to the electrodes, they spread as a result of diffusion and repulsion. An increase in the cloud size may result in charge collection by several neighbouring electrodes, and this phenomenon is called charge sharing. In this case, with no circuitry dealing with charge sharing, a detector may register more than one simultaneous event, and the signal amplitudes are no longer proportional to the deposited energy. Therefore, charge sharing may significantly distort the energy and spatial resolution, as well as result in an increase in the false counts within lower energies in the spectrum and a decrease in the number of counts in higher energies in the spectrum. To overcome problems caused by the charge sharing effect, on-chip hardware algorithms have been proposed, and some of them were implemented in silicon. In some applications, an off-chip correction of measured data is also possible. Solutions involve the process of estimating total charge based on fractional signals and assigning a hit to the pixel with the largest charge deposition. Alternatively, the pattern recognition technique, or searching the centre of charge-cloud gravity, has been proposed. Performing these tasks always requires the development of a large inter-pixel communication system. Interestingly, even though the charge sharing effect has a negative impact on the spatial resolution of a detector, the resolution can be improved beyond the resolution determined by the physical pixel size when information on the proportions of charge collected by neighbouring pixels is used to estimate the position of the event. This chapter presents the physics of the charge sharing effect, discusses different implementations that attempt to overcome charge sharing, and possible ways of using the charge sharing effect to the advantage of the detectors.

2 Charge Sharing Physics and Modelling In a direct detector, X-ray photons are absorbed and directly converted into electronhole pairs, whose number depends on the sensor material and the photon energy. A hybrid pixel detector, working in the SPC mode, consists of a segmented sensor connected to an array of electronic readout channels with a bump-bonding technique, which is presented in Fig. 1. A sensor is a system of reverse biased diodes and a high resistivity pure layer is used to provide detection with low leakage current. A bias voltage is applied to drift charge carriers and induce signals at the electrodes for processing by the readout electronics. In an SPC device, each photon is processed individually and generally both the interaction position and photon energy can be measured. However, if the charge cloud produced by an interacting photon spreads out during the drift to the electrodes, it can be detected by more than one channel of the readout ASIC. The charge sharing between pixels is presented in Fig. 1 for photon B.

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Fig. 1 Charge sharing effect in a hybrid pixel detector. Photon A hits the sensor in the pixel central area, thus, the charge is collected by only one electrode and processed by one readout channel. Photon B interacts on the pixel edge, and the fractional signals are processed by neighbouring readout channels

The charge cloud is commonly assumed to be Gaussian shaped [1]. The size of the cloud arriving at the electrodes can be modelled using a simple diffusion model and expressed in terms of the detector parameters, according to Eq. (1) which is based on the solution of the diffusion equation [2]:  σx =

.

2kT (d − λ)2 /qV =

√

2Dt,

(1)

or according to Eq. (2) [3]:  r = r0 + 1.15 2kT (d − λ)2 /qV ,

.

(2)

where σ x is charge cloud sigma, r is defined as the radius of the charge cloud, r0 is the initial charge cloud width formed in the sensor, d is the sensor thickness, λ is the photon interaction depth, V is the the bias voltage, k = 1.38•10−23 J·K−1 is the Boltzmann constant, T = 300 K is the temperature, and q = 1.602•10−19 C is the unit charge, D is the diffusion coefficient, t is the collection time. If the detector thickness d  λ, the particle mean free path λ is negligible. However, as shown in [4], absorption depth should be taken into account to process data for high resolution imaging. Thus, in the simple diffusion model for simulation purposes in the following paragraphs, the mean free paths λ were calculated from the cross sections obtained from the NIST X-ray attenuation database [5]. It was shown in [6] that the diffusion of the charge cloud is the main factor influencing the spread of the charge cloud, however, the analytical model underestimates the size of the charge cloud, which is affected by other processes such as repulsion, Compton scattering, and fluorescence. If more detailed calculations are needed, Monte Carlo simulations of photon transport and absorption in matter and charge carrier transport in the semiconductor sensor can be performed [6–8].

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3 The Significance of Charge Sharing Effect in Small Pixel Devices Based on the diffusion model the charge cloud sigma can be estimated for detectors depending on the sensor material, photon energy and sensor dimensions. To show how many photon interactions in a typical detector are subject to charge sharing the charge cloud sigma was estimated for two example sensors (Si and CdTe) of different thicknesses and bias voltages. The resulting charge cloud sizes with respect to pixel sizes are collected in Table 1. The pixel area not affected by charge sharing is defined as the pixel area for which 99.7% of the charges resulting from one interaction are processed by only one readout channel. Figure 2 visualises the charge cloud size with respect to the pixel size. The results show that for small pixel devices, with the 100 μm pixel pitch and smaller, the size of the charge cloud becomes significant relative to the pixel dimensions. Thus, the charge sharing effect needs to be considered and, preferentially, corrected by the dedicated algorithm. The next sections describe the aspects of detector operation influenced by charge sharing and the algorithms that allow to deal with charge sharing on and off chip.

Table 1 Pixel area affected by charge sharing for sample detectors Sensor material Photon energy (keV) Sensor thickness (μm) Bias voltage (V) Pixel size (μm) Calculated σ x (μm) Calculated σ x /pixel size Pixel area not affected by charge sharing

Detector 1 Si 8 320 100 100 5.75 0.058 43%

50 5.75 0.115 10%

Detector 2 CdTe 22 1500 −500 100 14.39 0.144 2%

50 14.39 0.288 0%

Fig. 2 Simulations of the charge cloud spread on the pixel for sample detectors described in Table 1. The blue circle represents the charge cloud of 3 sigma radius for a photon hitting the pixel centre. The gray square represents the pixel area not affected by charge sharing

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4 Influence of Charge Sharing on the SPC Detector Performance A typical readout channel of an SPC detector consists of a preamplifier, which is charge sensitive, a pulse shaper, which improves the signal-to-noise ratio, a discriminator, which compares the signal with a threshold and a digital circuit, processing and storing the information about registered events before transmitting it off-chip [9]. In the simplest implementation, a counter is incremented if the signal crosses the threshold. When charge sharing occurs, fractional signals are processed by neighbouring channels; thus, the same event might be registered multiple times or might not be registered at all, depending on threshold settings. This effect can be observed on the integral and differential spectra.

4.1 Impact on the Number of Registered Counts as a Function of Threshold Voltage The effect of charge sharing impacts the number of counts measured as a function of the threshold voltage, namely, an integral energy spectrum. The cascaded model of an SPC detector and simple linear charge division model [10, 11] defined by Eq. (3) can be applied to the measured characteristics. N (ET , EX ) =

.

      1 l ET ET − Ex 1 − 1−2 1 − Erf √ 2 x0 Ex 2 σ 2 

l σ − + √ e x0 Ex 2π

ET −Ex √ σ 2

2

(3)

where N is the counts number, ET is the energy threshold, Ex is the X-ray energy, l is the charge sharing region width, x0 is the pixel size, σ is the noise sigma. As stated by the authors of [12] the linear charge division model describing microstrip and large pixels detectors may be insufficient for small pitch pixel detector modelling (such as 25 μm pitch), since events occurring in the pixel corners become a significant part of interactions. The model can be extended in that case [12]. Figure 3 presents the measured data and the fitted model described by Eq. (3) for the detector consisting of LNPIX ASIC [13] and a 320 μm thick silicon sensor, biased with voltages of 62 V and 326 V illuminated with 8 keV photons. The charge sharing can be observed on the integral spectrum as the characteristic slope dependent on the bias voltage. Low bias leads to a larger charge cloud and more significant increase of the registered events in the low energy range and a decrease of the counted events in the high energy spectrum. In the differential spectrum, the charge sharing effect manifests itself in the characteristic plateau

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Fig. 3 Measurements of an X-ray detector with LNPIX ASIC and Si sensor biased with low and high voltages (a) integral spectra – measurements and fitted model, for the reference no charge sharing case was also modelled. (b) differential spectra

Fig. 4 The total number of counts registered in the detector as a function of beam position for CHASE Jr. chip (a) in the SPC mode and (b) with the charge sharing correction algorithm

with the higher number of counts, the lower the bias voltage. The reason for this behaviour is distorted by charge sharing events registration on pixel edges.

4.2 Impact on the Number of Registered Counts as a Function of Photon Interaction Position The effect of counts loss can be also observed in the tests with precise, pencil photon beam scanning the area of the detector. The results of such tests in synchrotron with the X-ray detector consisting of a Chase Jr. chip [14] and a 320 μm thick Si detector are presented in Fig. 4. The measurements are performed for set threshold in two operating modes, namely single-photon-counting with no charge sharing correction and with the C8P1 charge sharing correction algorithm enabled. Table 2 presents the mean and standard deviation of the number of counts registered by the detector in the chosen region of interest (ROI) for the test results presented in Fig. 4.

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Table 2 Number of counts in the chosen regions for the chase Jr. chip working with and without charge sharing correction [14] Mode of operation and region of interest Charge sharing correction OFF, all area Charge sharing correction ON, all area Charge sharing correction OFF, pixel central area Charge sharing correction ON, pixel central area

No of counts Mean 5404 5827 5822 5819

No of counts Sigma 1048 108 83 101

The results in Table 2 and Fig. 3 show that the number of counts registered by the detector is comparable when the charge sharing correction is enabled or disabled if the photon beam reaches the central pixel area. It stays on the same level also for the whole ROI including edges only if the charge sharing correction is enabled. If the entire detection ROI is examined, the total number of counts decreases when the charge sharing correction is disabled. Such problems with counting events on pixel borders lead as a consequence to the degradation of spatial resolution and detection efficiency. Therefore, the results prove the importance of charge sharing correction algorithms, especially for small pixel devices and thick sensors, for which the charge sharing is more profound.

5 Algorithms Dealing with Charge Sharing 5.1 Known Solutions Implemented on Chip A possible way to overcome limitations caused by charge sharing is to introduce advanced counting algorithms in the readout electronics. Known approaches to charge sharing mitigation are presented in Table 3. Most algorithms [14–19] are based on the summing concept. The fractional signals from the adjacent pixels are added, and the total recovered signal undergoes discrimination. The pixel from the neighbouring group that received the majority of charge is chosen either by comparison of signal amplitudes between the pixels or using the Time-over-Threshold technique. Other solutions [20, 21] implement pattern recognition algorithms [23, 24], which together with signal summing, allow for event position and total energy reconstruction. Another approach [22] involves the approximation of a geometric shape of a charge cloud by finding the centre of gravity of an object. Several concepts are proposed or compared in simulations [25–27]. It should be noted that charge sharing correction, especially involving analog summing, requires implementation of complex inter-pixel communication and pixel-to-pixel calibration techniques (such as DC offsets and gains correction) [28].

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Table 3 Algorithms implemented on the chip for charge sharing correction

ASIC Pixirad Pixie III [15] X-Counter [16]

No of pixels 512 × 402

Pixel size [μm2 ] 62 × 62

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64 × 64 16 × 16

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Charge reconstruction technique Pixel summing mode Charge sharing correction feature Charge summing algorithm Charge summing algorithm C8P1 C8P1 Multithreshold pattern recognition Pattern recognition COGITO algorithm

5.2 Algorithms Limitation – High Count Rate Performance The solutions dealing with charge sharing implemented on chip allow to allocate the event to the pixel receiving majority of charges from the charge cloud. Additionally, if they involve summing, the total photon energy can be retrieved. However, the analog summing blocks the front-end of neighbouring pixels for the time of charge correction algorithm processing, which results in increasing the pile-up effects and, as a consequence, increasing the dead time of the detector. For example, the average dead time for the C8P1 algorithm, estimated from the Chase Jr. chip measurements using the paralyzable detector model, was τ = 1.01 μs, for the SPC mode, τ = 0.21 μs [14]. The dead time measured for the Medipix chip was τ = 2.02 μs, in the charge summing mode, and τ = 0.4 μs, for the SPC mode [29]. The dead time of the detectors with pattern recognition algorithm, which involves summing, also increased compared to the SPC mode, and the high count rate performance depended on the pulse shaping time and the charge cloud sigma [30]. Figure 5 presents the simulated output vs. input count rates for the detector with the pattern recognition algorithm implemented. Limitation of the high count rate performance due to the charge summing techniques leads to research on new mechanisms that do not increase pile-up, such as the coincidence counting bin, which is triggered by coincident events in adjacent pixels and provides an estimate of the double counts arising from charge sharing [31].

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Fig. 5 Simulations of high count rate performance of a hybrid pixel detector working in an SPC mode and with the pattern recognition (PR) algorithm. (Results from [30])

6 Subpixel Algorithms Improving Spatial Resolution It was shown in previous sections that the counting performance of the SPC detectors suffers from charge sharing in small pixel devices. The solution to this problem is implementation of the charge sharing correction algorithms inside the readout electronics, which allows for proper spatial allocation of the event and photon energy reconstruction. However, even though the charge sharing effect has a negative impact on the spatial resolution of a detector, the resolution can be improved beyond the resolution determined by the physical pixel size when information on the proportions of charge collected by neighbouring pixels is used to estimate the position of the event [32]. So far, the off-chip method has been presented to acquire high-resolution two-dimensional images with integrating pixel and strip detectors equipped with MONCH and GOTTHARD chips, respectively [33]. Since the proposed clusterfinding algorithm is dedicated to integrating detectors, it must deal with the noise and integration of dark current that happens during exposure. Another challenge is to acquire large statistics for complete image reconstruction. For the measurements of the detector consisting MÖNCH chip, the spatial resolution of 3.5 μm was achieved for the pixel pitch of 25 μm [34]. The same research group presented in the [35] the first implementation of the on-chip interpolation algorithm for a microstrip single-photon-counting MYTHEN III microstrip detector. A one-dimensional digital communication scheme between neighbouring channels was implemented. Each readout channel consists of two comparators and three counters, and the logic could be extended to the pixel detectors, however, it would require implementation of more complex interpixel communication and additional logics for photons hitting pixel corners, and would take up more silicon area.

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7 Conclusions Single-photon-counting systems suffer from charge sharing effect, which results in the deterioration of spatial and energy resolution of the detector. The smaller the detector pixel and the larger the charge cloud that reaches the electrodes, the more severe the impact of the charge sharing effect. It was shown that even for typical detectors of 100 μm pitch, most of the photon-sensor interaction results in charge division between channels. Therefore, it is necessary to implement dedicated algorithms to deal with this effect. The charge sharing correction algorithms require often complex mixed signal circuitry fitted inside each pixel. Implementation of such solutions allows reconstruction of both initial photon energy and interaction position, leading to the improvement of detector efficiency and spatial resolution. However, it should be noted that algorithms based on analog summing deteriorate the high count rate performance of the detectors and increase their dead time. Although the charge sharing effect has a negative impact on detector performance, it can be used to the advantage of the detectors, if the information on proportion of charges collected in the neighbouring pixels is used to estimate the photon position.

Acknowledgements This work was supported by the National Science Centre, Poland, under Contract No. UMO- 2018/29/N/ST7/02770.

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Sub-pixel Sensing for Pixelated CdZnTe Detectors Yuefeng Zhu

1 Introduction The performance and imaging capability of CdZnTe (CZT) detectors have improved steadily over the past decade at University of Michigan [1–9]. Energy resolutions around 1% FWHM at 662 keV have been consistently demonstrated using large volume (1.5.×1.5.×1.0 cm.3 or 2.0.×2.0.×1.5 cm.3 ) pixelated CZT detectors. An energy resolution of 0.48% FWHM at 662 keV for single-pixel-triggered events (or single-pixel events as we call) has been measured on a 2.0.×2.0.×1.5 cm.3 crystal using BNL readout ASIC system [10]. With a lower 1.5-keV electronic noise, the IDEAS VAD_UM digital ASIC with direct-attachment configuration can give 0.31% FWHM at 662 keV [11]. This resolution is already close to the 0.2% theoretic limit of the CdZnTe detectors. These Pixelated CZT detectors are capable of providing 3-D position information of gamma-ray interactions within one detector volume. It is a key performance parameter for Compton imaging or coded aperture applications [12]. The lateral position resolution of CZT detectors using pixelated anodes is limited by the pixel pitch. In the pixelated CZT detector design at University of Michigan, the pixel pitch is 1.72 mm. As a comparison, the depth sensing technique based on the cathodeto-anode ratio [1] can give about 0.5 mm depth resolution [10]. It is much more precise than the pixel pitch. The relatively poor lateral position resolution limits the Compton image angular resolution to roughly 40 degrees FWHM using simple back-projection reconstruction [13]. For coded aperture imaging, the impact is more significant [14].

Y. Zhu () University of Michigan, Ann Arbor, MI, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_3

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Better position resolution is desired to improve the imaging capability. A number of efforts have been made in the past decades to achieve position resolution better than the pitch of the charge collecting electrode for semiconductor detectors. Warburton [15], Burks et al. [16] and Williams et al. [17] proposed and demonstrated a method to obtain improved position resolution based on induced transient signals on non-charge-collecting electrodes in striped CdZnTe and HPGe detectors. Marks et al. [18], Vickersa and Chakrabarti [19] and Jakubek and Uher [20] studied several algorithms to achieve sub-pixel position resolution when an electron cloud is collected by several pixels in pixelated detectors. Narita et al. [21] showed the difference in the transient signals on neighboring non-charge-collecting pixels in pixelated CdZnTe detectors when the gamma-ray interaction position was changed. For our detectors, the pixel size of the anode is 1.72 cm as mentioned above. It is bigger than or similar as the electron cloud size in the energy range of 0–3 MeV, the dynamic range of our detector system [22]. Therefore, the charge-sharing sub-pixel position determination method discussed in [18–20] can’t be applied. The transient signal method mentioned in [16, 17] is promising. As mentioned in [21], the induced transient signals on the neighbor pixels change with the electron cloud location. However, since the area of a pixel in our detectors is much smaller than the area of the anode strip in [16, 17], the induced transient signals on the non-collecting electrodes are expected to be much smaller. It is more challenging to implement the transient signal method in the pixelated CdZnTe detectors. This article describes the detailed study on a sub-pixel position calculation algorithm based on non-charge-collecting transient signals [16, 17] for pixelated CdZnTe detectors. First, a detailed simulation to generate the signal pulse waveforms expected from the detection system is presented. Next, several subpixel position calculation algorithms are proposed for single-pixel events, which, combined with results from simulations, provides the theoretical limit on the best achievable position resolution as a function of electronic noise and energy deposition. These simulation results are then compared with the experimental data from a 2.0 cm.×2.0 cm.×1.5 cm CZT detector irradiated with a .137 Cs 662 keV gamma-ray source collimated by a tungsten collimator with a 100 .μm opening. The result validated the accuracy of the proposed sub-pixel calculation methods. Finally, a method for measuring sub-pixel positions for two-pixel triggered events (or twopixel events as we call) is presented and discussed.

2 The Detector System An illustration of a 3-D position-sensitive CZT detector is shown in Fig. 1. The CZT detector used in this study is 1.5 cm thick and its dimension is 20.×20.×1.5 mm.3 . The cathode is a simple continuous plane, while the anode consists of an array of 11 .× 11 pixels. Each pixel is 1.66 .×1.66 mm.2 with a gap of 60 .μm between the pixels. The pixel pitch is 1.72 mm. The guard ring is 0.5 mm wide. It is used to reduce the leakage current from the side surface of the crystal. The guard ring can be biased

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Fig. 1 An illustration of the pixelated CdZnTe detector used in this study

up to a certain voltage to steer the electron cloud toward inner pixels to improve the detector efficiency [23]. The readout electronics of the pixelated CdZnTe detectors are ASIC based systems. Several readout ASICs have been developed at University of Michigan [1, 24–26]. An ASIC called VAD_UM ASIC [26, 27] is used in this study. It was jointly developed by University of Michigan, USA and IDEAS, Norway. This ASIC is consisted of 130 channels with pre-amplifiers and waveform sampling circuits in each channel. When an event happens, the induced signal waveforms can be sampled and stored in the ASIC. There are 160 sampling capacitor cells for each channel. The sampling frequency is up to 80 MHz and can be changed to a lower frequency to cover the entire charge drifting window. The stored waveform samples are analog signals. They can be readout and digitized by an external ADC. A FPGA is required to control the process. The VAD_UM ASIC is also called digital ASIC because of its waveform sampling capability. The VAD_UM ASIC has four dynamic ranges: 700 keV, 3 MeV, 7 MeV and 9 MeV. The power consumption is very low, only about 1.6 mW per channel. The ASIC can work in either full readout mode for system calibration or sparse readout mode for applications. The electronic noise of the system was measured to be about 2 keV in full readout mode when the ASIC was attached to a CdZnTe detector and the detector was biased. In this article, a prototype digital readout system was built for a .3 × 3 pixel array for the principle study. The details of this system are given in Sect. 6.1. The VAD_UM digital system was used for the charge-sharing sub-pixel study.

3 System Modeling A simulation was performed to find expected pre-amplifier output pulse waveforms. These simulated waveform results are then be used to develop and optimize the subpixel position estimation techniques for experimental data. The simulation package includes two components: charge transport and induction and electronic noise.

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3.1 The Signal Induction Charge induction on a given electrode can be calculated using the Shockley-Ramo theorem [28]. Barrett et al. showed an example to calculate the charge induction on electrodes [29]. Kim [22] described in detail a simulation procedure applied for pixelated CdZnTe detectors. This article uses a similar simulation method as Kim. In the following paragraphs, we will give a simple description of the method. The track and velocity of electrons and holes are determined by modeling the operating electric field in the detector. It is assumed that electrons and holes are following electric field in the crystal bulk. When the charge reach electrode surface, holes are just simply collected by cathode. However, for electrons there are two boundary conditions defined to describe their behavior at anode surface based on grid bias. If grid is biased, we will assume full charge collection. Electrons that reach the gap instead of pixel pads or grid will be further transported along the electric field between grid and pixels on the anode surface; If grid is unbiased, electrons will stay in the location where they reach the anode surface. The induced charge on each electrode is calculated from the weighting potential along each charge track. The final induced signal at time t is then equal to the product of the charge quantity and the difference in weighting potential between the charge carriers position at time t and its initial position. The operating and weighting fields are complicated in a pixelated detector. This problem is solved numerically using an electromagnetic field calculation software: Maxwell v11 from Ansoft. Figure 2 gives an example of the simulated waveform signal induced on a center collecting pixel as well as the pixels that surround it. In this example, each electron cloud is modeled as a geometrical point with a total charge equivalent to the energy deposition of a 662-keV photon. Two electron clouds are simulated in this figure, one is located at the center of the collecting pixel (thick line) and another is near the pixel edge (dashed line). They are both in the middle depth of the detector. For this simulation, the cathode bias is .−3000 V. Because the mobility of holes is much lower than that of electrons, only the electron drift was simulated during the charge collection time. The trapping of electrons in the detector is not modeled because it is not a critical factor in this study as will be discussed in Sect. 5. The signal induced on the center collecting pixel is very small in the detector bulk until the electron cloud drifts to the vicinity of the pixelated anode. In this anode region, the induced signal rises rapidly because of the large gradients in weighting potential and eventually, it will rise to an amplitude close to the original 662 keV. There is a small amplitude deficit due to the trapped holes in the detector bulk. Additionally, electron trapping can contribute to the deficit of the induced signal amplitude. For the non-collecting neighboring pixels, the signals first rise as the electron cloud travels from the detector bulk to near the anode surface and then drop when the electron cloud enters the anode region. The boundary of the anode region is defined as the depth where the maximum of this “transient signal” happens, roughly one pixel size away from the anode surface. Eventually, the signals will drop to zero or

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to a negative value (hereafter referred as a “negative tail”) due to the trapped holes. The amplitude of the negative tail depends on the depth of the initial interaction. When the interaction happens at the cathode surface, the neighboring pixel signal will drop to zero. If the interaction is in the detector bulk or the anode region, the negative tail occurs. The negative tail is the biggest if the interaction happens at the anode region boundary. The peak signal amplitude of the neighboring pixel’s transient waveform is very sensitive to the lateral position (or sub-pixel position) of the interaction position. As seen in Fig. 2, the induced signal on the neighboring pixels changes significantly from the thick line to the dashed line when the electron cloud moves from the pixel center to the edge. The reason is that when a transient signal reaches its maximum the distance between the electron cloud and a neighboring pixel depends significantly on lateral interaction position. As was mentioned earlier, the transient

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signal reaches its maximum when the electron cloud is roughly one pixel length away from the anode. At this time, the lateral distance from the electron cloud to the center of a neighboring pixel ranges from half a pixel to one-and-a-half pixels for interaction location on one edge of the charge collecting pixel or the other. As a result, the total 3-D distance from the electron cloud to a neighboring pixel at the transient peaking time strongly depends on the lateral position of the electron cloud at that time. Therefore, the peak amplitude of the neighboring transient signals actually gives the lateral position where the electron cloud enters the anode region. An interaction location is the start point of an electron cloud trajectory. if an electron cloud trajectory is a straight line perpendicular to the cathode and anode surface, the neighboring transient signal peak amplitudes would be directly related to the initial lateral interaction position. However, the electron cloud trajectory can be bent because of grid bias or material defects. The impacts of those factors on neighboring pixel transient signals are different. The grid bias is used to help improve charge collection efficiency and it is normally very small comparing to the cathode bias. Its impact on an electron cloud trajectory is negligible before the electron cloud gets very close to the anode surface, so the initial interaction position can still be obtained by the neighboring transient signals. As for material defects, it can alter an electron cloud trajectory significantly when the electron cloud is still in the detector bulk. In this case, the neighboring pixel transient signals won’t be able to provide initial interaction positions. If a detector crystal has very good quality and is free of defects, we can use the peak amplitude of the transient signals to determine the sub-pixel position of an interaction. However, as we can see in Fig. 2, the transient signals are very fast and have very small amplitude compared to the charge collection signal. Electronic noise is expected to be the limiting factor in how accurately we can determine the sub-pixel interaction position.

3.2 Electronic Noise Simulation Pullia and Riboldi [30] provide a method to precisely simulate the electronic noise of a detector system in the time domain. Simulation of the parallel and serial noise in our detector system is based on experimental data. The 1/f noise, is assumed to be negligible for our first-order approximation. In this case, the noise parameters that need to be constructed for the noise model are the parallel- and serial-noise amplitudes, which are assigned to a and b respectively. The noise density function can be written as S 2 = a 2 + b2 /ω2 .

.

(1)

Where .S 2 is in unit of .keV 2 /H z and .ω is the circular frequency. To measure a and b, we can apply a CR-RC.4 filter to the signal waveform and search for the lowest noise amplitude .Vn and the corresponding shaping time .τopt . The noise amplitudes

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45

can then be calculated as a 2 = Vn2 × τopt × C1 .

(2)

b2 = Vn2 /τopt × C2 ,

where .C1 and .C2 are the coefficients calculated from the response function of the filter. For a CR-RC.4 filter, .C1 and .C2 are 220 and 31.4 respectively. If a different filter is applied, .C1 and .C2 would have different values. The near-optimal shaping time of a CR-RC.4 filter for the collecting pixel signal was measured to be about 250 ns (at a peaking time of 1 .μs) and the noise FWHM was 4 keV. With these parameters, a general noise model can be constructed for the waveform model.

3.3 Digital Filter Design To compare the performance of estimating the transient signal amplitude on neighboring anode pixels, several digital filters, including CR-RC, triangular, and the theoretical optimal filter, were studied. The theoretical optimal filter is obtained based on the method described by Radeka [31]. For collecting pixels, the signalto-noise ratio of the optimal filter is shown in Fig. 3a. However, the optimal filter formula described in [31] cannot be directly applied to the neighboring transient signal. In [31], the signal amplitude is chosen to be the maximum value of the filtered signal. However, as will be discussed in Sect. 4, it is the difference between the maximum and minimum value of the filtered transient signal that provides a useful transient signal amplitude. In this case, the signal amplitude for transient signals can be written as vo = vo (tmax ) − vo (tmin )  ∞ . 1 H (ω)Vi (ω)(ej ωtmax − ej ωtmin )dω. = 2π −∞

Signal to Noise Ratio

(a) 600

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Fig. 3 The signal-to-noise ratio of different shaping filters for: (a) the charge-collecting pixel signal, and (b) the non-collecting pixel transient signal

(3)

12 10 8 6 4 2

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Here, .vo (tmax ) and .vo (tmin ) are the signal maximum and minimum. .H (ω) is the Fourier transform of the filter and .Vi (ω) is the Fourier transform of the noisefree transient signal profile (or the mean input signal). If we know the noise power density function .Si (ω), the noise amplitude can be calculated as .

Vn2 =

1 2π



∞ −∞

|H (ω)|2 Si (ω)dω

(4)

The signal to noise ratio can then be expressed as   ∞ j ωtmax − ej ωtmin )dω2  vo2 −∞ H (ω)Vi (ω)(e .η = , = ∞ Vn2 2π −∞ |H (ω)|2 Si (ω)dω 2

(5)

The optimal signal-to-noise ratio [31] occurs when the frequency response of the filter is Vi∗ (ω) −j ωtmax (e − e−j ωtmin ) Si (ω)  V ∗ (ω) −j ωtmax  e 1 − e−j ω(tmin −tmax ) . =k i Si (ω)

H (ω) = k .

(6)

Vi∗ (ω) is the conjugate of the Fourier transform of the input signal, k is a constant, and .e−j ωtmax is a time-shift term. Neither k nor .e−j ωtmax affect the signal-to-noise ratio, thus, they can be eliminated to simplify the equations. Hence, the optimal filter for neighboring pixel signals is

.

.

nb Hopt (ω) =

 Vi∗ (ω)  1 − e−j ω(tmin −tmax ) . Si (ω)

(7)

The time interval between occurrence of the maximum and minimum signal amplitude of the shaped transient signal depends on the digital filter. As a result, it is difficult to analytically derive the solution for an optimal filter. However, a solution can be found numerically by searching through all possible time intervals. The dashed line in Fig. 3b gives the signal-to-noise ratio of the optimal filters for simulated neighbor transient signals. The best signal-to-noise ratio can only be achieved with the optimal filter. As Fig. 3b shows, the CR-RC filter performs better than the other three filters and its best signal-to-noise ratio at the shaping time of 200 ns is very close to the optimal filter. Because the transient signal pulse waveform is a sensitive function of the 3-D position of interactions, it is very difficult to apply the optimal filter to calculate the sub-pixel position experimentally. Therefore, we use a CR-RC filter for the transient signal filter as a good practical approximation. Based on the results in Fig. 3b, it is possible to achieve position resolution similar to what can be obtained using the optimal filter.

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4 Sub-pixel Position Calculation Algorithm The maximum amplitude of the transient signals of the 8 neighboring pixels can be compared quantitatively to determine the sub-pixel position of an interaction. However, the transient signal maximum decreases as the interaction position changes from the cathode side toward the anode side. The signal becomes very small when the interaction is in the anode region. If we choose the signal maximum to calculate the sub-pixel position, the algorithm coefficients may vary from depth to depth and the sub-pixel position resolution will be poor in the anode region. Fortunately, the signal maximum occurs in a certain depth for the interactions located at a particular lateral position, where the electron cloud just drifts past the boundary of the anode region. The weighting-potential change from this depth to the anode surface (charge fully collected) is independent of the initial depth of the electron cloud when this interaction occurs in the detector bulk. In other words, the signal difference between the signal maximum and its negative tail, the signal minimum, is not a function of interaction depth at a particular lateral position and in detector bulk. Therefore, we define the transient signal amplitude as the value difference between the signal maximum and minimum amplitudes. In the anode region this transient signal amplitude is no longer independent of interaction depth. However, it is still much bigger than the transient signal maximum, which is actually zero and thus this definition extends the active region where we can perform subpixel position calculation. Transient signal amplitude is the key measurable parameter that is used to calculate sub-pixel interaction position. A method referred to as the opposingneighboring ratio uses these neighbor pixel amplitudes to calculate the sub-pixel centroid position of an electron cloud. If the position of the center collection pixel and its 8 neighbors is labeled as shown in Fig. 2, the opposing-neighboring ratio along the lateral x direction, .Rnx can be written as Rnx (x, y, z) =

.

s21 (x, y, z) − s23 (x, y, z) , s21 (x, y, z) + s23 (x, y, z)

(8)

where .s21 (x, y, z) and .s23 (x, y, z) are the transient signal amplitudes on the middleleft and the middle-right neighbors respectively induced by an electron cloud located at (x,y,z). As described above, the transient signal amplitude is not a function of depth z unless the interaction happens in the anode region. Therefore, Eq. (8) can be simplified as Rnx (x, y) =

.

s21 (x, y) − s23 (x, y) . s21 (x, y) + s23 (x, y)

(9)

Here, .Rnx is not only a function of the lateral x coordinate of the electron cloud, but also the lateral y coordinate. If a electron cloud is moving along the y direction, its distance to the middle-left neighbor (pixel 21) and middle-right neighbor (pixel 23) will change, resulting in different induced signals on those neighbors. However,

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if the left three neighbors and right three neighbors are considered as a whole respectively, the mean distance from the moving electron cloud to these neighbors will change much less. Therefore, a new signal ratio can be written as sl (x) ≈ sl (x, y) =s11 (x, y) + s21 (x, y) + s31 (x, y) .

sr (x) ≈ sr (x, y) =s13 (x, y) + s23 (x, y) + s33 (x, y) sl (x) − sr (x) Rx (x) = . sl (x) + sr (x)

(10)

We call this the opposing-neighboring ratio. The relationship between .Rx and the x coordinates is calculated by simulation for different lateral y positions and depths z. The result is presented in Fig. 4. The change in .Rx due to the variation of the lateral y position and the depth z of an interaction is given by the error bar. As can be seen, such change is small compared to the pixel size, indicating that the approximation of Eq. (10) is valid. Additionally, Fig. 4 shows that the .Rx versus x curve is close to a straight line. To a first order approximation, we can employ a linear function to model the signal ratio .Rx versus x in the sub-pixel position calculation. In the y direction, the opposing-neighboring ratio .Ry can be formed the same way as for .Rx : st (y) ≈ st (x, y) =s11 (x, y) + s12 (x, y) + s13 (x, y) .

sb (y) ≈ sb (x, y) =s31 (x, y) + s32 (x, y) + s33 (x, y) st (y) − sb (y) Ry (y) = . st (y) + sb (y)

(11)

0.8

Opposing Neighboring Ratio

0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1

−0.5 0 0.5 X Coordinate of the Interaction Position (mm)

1

Fig. 4 The relationship between the opposing-neighboring ratio .Rx and real lateral x coordination calculated by simulation. The curve gives .Rx as a function of x when the electron cloud is in the middle of a pixel (.y = 0) and near the cathode surface (.z = 0). The error bars mark the range of the .Rx if the lateral y position and the depth z of the electron cloud change in the pixel volume. The dashed lines mark the boundary of a pixel

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Besides the opposing-neighboring ratio, there are at least two more ratios that can be used to calculate the electron cloud position: 1. the ratio between the neighboring pixel signals and the center pixel signal 2. the signal ratio between two corner neighbors and the center pixel signal. We refer to (1) as the neighbor-to-center ratio, and (2) the corner-neighbor ratio. The neighbor to center ratio (.Rcx and .Rcy ) and corner neighbor ratio (.Rcrx and .Rcry ) are expressed as Rcx (x) = .

sl (x) s22

st (y) Rcy (y) = s22

(12)

and Rcrx (x, y) = .

s11 (x, y) − s13 (x, y) s22

s11 (x, y) − s31 (x, y) Rcry (x, y) = s22

(13)

where .s22 is the charge collected by the center pixel. These two methods have their shortcomings. For the neighbor-to-center ratio, the ratio is not a linear function of the actual electron cloud position. For the corner-neighbor ratio, the ratio is a function of both x and y coordinates and thus is difficult to calibrate. Therefore, the opposing neighbors’ transient ratio is preferred. However, neighbor-to-center ratio and corner-neighbor ratio require fewer neighboring pixel signals than the opposing-neighboring ratio. The neighbor-to-center ratio requires three neighbors on one side of a collecting pixel. The corner-neighbor ratio method requires two corner neighbors. For multi-pixel interaction events, the induced signal on a neighboring pixel from a electron cloud may be polluted by the signal induction from another separate electron cloud. In this situation, opposingneighboring ratio may not be applicable and then the neighbor-to-center ratio or corner-neighbor ratio could be employed to determine the sub-pixel position for each electron cloud. Section 7 addresses this scenario in greater detail.

5 Estimate of Sub-pixel Position Resolution by Simulation The precision of the sub-pixel position obtained by the opposing-neighboring ratio method can be estimated based on the system model discussed in Sect. 3. The results are given in Fig. 5. In this simulation, the energy deposition of the gamma ray is set to be 662 keV and the electronic noise is set to 4 keV FWHM. The cathode is

50

Y. Zhu (a) Xmeasured−Xtrue (mm)

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Fig. 5 Sub-pixel simulation performance results: (a) the offset difference between the mean calculated position and the true simulated position based on the linear assumption, and (b) the position variation in terms of FWHM due to 4 keV electronic noise. The offset and position variation is plotted for the x coordinate. The error bars mark the offset and FWHM range as the electron cloud position is shifted along y and z directions through the volume of the collectingpixel column

assumed to be biased at .−3000 V and the grid is at .−100 V. The sampling frequency is set as 100 MHz. The energy is assumed to be deposited at a single space point rather than a extended electron cloud for principle study. Figure 5a gives the bias of the calculated position using the linear-relation assumption of .Rx (as defined in Eq. (10)) versus x from the true energy-deposition position. Figure 5b presents the calculated sub-pixel position uncertainty due to the 4 keV electronic noise. The calculated position bias is smaller than the position uncertainty, indicating that the linear assumption is an appropriate model. The dominant source of uncertainty in the calculated sub-pixel position is the electronic noise. Uncertainty in the collected charge due to charge production in the ionization process and charge trapping will generate proportional changes to the signals induced on all 8 neighbors. As a result, the associated fluctuation cancel out using the signal ratio. As seen in Fig. 5b, the expected sub-pixel position resolution at 662 keV is below 180 .μm. This simulation result assumes energy is deposited at a single point. In reality, energy is deposited in an extended electron cloud. The calculated sub-pixel position for a real interaction is the centroid of the electron cloud. As a result, the size of the electron cloud will introduce additional uncertainty in the determination of the interaction position.

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6 Experimental Measurements and Analysis 6.1 Measured Sub-pixel Position Resolution with Collimator Results from a collimation experiment provide an experimental measure of the subpixel position resolution. Figure 6 illustrates the design of the collimator experiment. The collimator is made of 6-cm thick tungsten with a 100-.μm opening, separated by 3 cm away the bottom surface of the detector. The opening of the collimator is aligned parallel with the edge of a target pixel. A .137 Cs point source is placed in the collimator and used to irradiate a narrow section of the pixel from the cathode side of the detector. The irradiated pixel and its 8 neighbors are connected to eVProducts model 5093 preamplifiers. Each preamplifier signal is fed into a channel of a GaGe Octopus CompuScope model 8389 multichannel digitizer card (8 channels per card, 14-bit resolution, 125 MHz), operating at a 100 MSa/s sampling rate (10-ns sampling interval). The detector is manufactured by eV-Products. The detector schematics are identical to those found in the system model discussion in Sect. 3. During operation, the cathode is biased at .−3000 V but the grid was unintentionally left unbiased. However the different grid bias shouldn’t impact the conclusion we have achieved in the simulation. The collimator is positioned near the center of the pixel at first and then moved toward the edge with a step size of 100 .μm. For each collimator position, photopeak events from single-pixel interactions are selected for use in the sub-pixel study. For neighbor-pixel signals, a CR-RC filter with 200-ns shaping time is employed. This

Fig. 6 The collimator design for experimentally measuring sub-pixel position resolution

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(b)

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Fig. 7 Measured sub-pixel resolution at 662 keV: (a) the mean neighboring pixel ratio for each collimator position. This data is fitted by a linear function and the result shows the slope as .(9.2 ± 0.5) × 10−4 and the interception as .0.072 ± 0.009 with 95% confidence; (b) the FWHM of the position variance at each collimator position. The origin of x axis of these plots are the start location of the collimator instead of the center of the pixel

filter choice is based on the simulation results described in Sect. 3.3. The results of the measurements at four collimator positions are summarized in Fig. 7. Figure 7a shows the opposing-neighboring ratio for each collimator position and Fig. 7b gives the measured position uncertainty. The x axis origin of both plots are the start location of the collimator. The FWHM of the position estimate is below 360 .μm. However, this 360-.μm position uncertainty is not equivalent to the sub-pixel resolution. There are two more factors that add uncertainty to the measurement: (1) collimator-beam size and (2) electron cloud size. The collimator has a 100-.μm opening, but the beam will be spread bigger at the detector surface and the beam size will become even wider when the interactions occur at deeper depths in the detector. The increase in measured resolution caused by the collimator is significant. Additionally, the measured sub-pixel position of each interaction represents the centroid of the ionized electron cloud not the initial gamma-ray interaction position. As a result, even when the gamma beam is fixed at a single position relative to the detector, the electron cloud centroid will be different if the secondary fast electron follows a different track. Using the Geant4 simulation package, we can simulate the total uncertainty contribution from the two factors together. As shown in Fig. 8, we find that the collimator beam and 662-keV electron cloud can cause 280-.μm FWHM position uncertainty in the measurement. The contributions of spreading from collimator and electron cloud size can be simulated individually and the result shows collimator can cause 150 .μm spreading in FWHM and electron cloud size introduces 240 .μm. Though both collimator and electron cloud caused spreading are not strictly Gaussian shaped, the quadratic sum of the contribution from collimator and electron cloud results in the same result as obtained with the simulation considering them together, indicating quadratic operation can be applied in estimating the contribution of each factor to sub-pixel position resolution measurement.

Sub-pixel Sensing for Pixelated CdZnTe Detectors 50 simulated data Gaussian fit

45 40 35

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Fig. 8 The simulated distribution of the electron cloud centroid from a 662-keV gamma-ray source using a collimator. Distribution width is due to the collimator and electron cloud size

53

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After quadratic subtraction, the real sub-pixel resolution of the system in terms of determining electron cloud centroid position is calculated to be around 230 .μm at 662 keV. However, if we consider the initial gamma-ray interaction position, we would need to add the additionally uncertainty caused by electron cloud size. The projection of electron cloud size on x-y plane is a function of recoil electron direction, especially at high energy. If assuming the secondary electrons are emitted isotropically, the sub-pixel position resolution of initial gamma-ray interaction position would be 330 .μm FWHM at 662 keV. The 230-.μm sub-pixel position resolution at 662 keV is a little bit worse than the simulation result of 180 .μm. There are several factors that may cause the difference, including the inaccuracy of the measured geometry of the collimator setup (especially the distance between the detector and the collimator and the opening width), slight skewing of the collimator beam, the neglected .1/f noise, the diffusion of the electron cloud and material defects. The inaccuracy of the measurement on geometry setup can be estimated in a easy way. The spreading caused by the collimator should be proportional to .δ × (d + z)/z, where .δ is the opening width, d is the distance between collimator surface and detector surface and z is the collimator thickness. It can be calculated that even with 1 cm error on d or z, the change of total uncertainty caused by collimator and electron cloud would be smaller than 20 .μm. For opening width .δ, the error of measurement should be less than 10% and its influence on total uncertainty can be calculated to be smaller than 20 .μm too. Therefore, the geometry measurement error should be negligible. Diffusion can change the drifting path of electrons [32]. For our 1.5 cm CdZnTe crystals at 3000 V, diffusion caused position uncertainty for each electron would be about 70 .μm in standard deviation and thus 170 .μm in FWHM if assuming Gaussian distribution. However, ideally diffusion shouldn’t shift the centroid of an electric cloud if the electron cloud is consisted of infinite number of electrons. In reality we expect additional uncertainty from diffusion but its impact on sub-pixel position resolution should be much smaller than 170 .μm and we expect its impact on the measurement uncertainty should be negligible. The presence of .1/f noise may change the performance of the CR-RC filter and cause some underestimation of the uncertainty from the electronic noise in simulation. At last, the material defects in CdZnTe has been known for deviate electrons from

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drifting straight [33]. In a poor crystal, this effect can move electron several hundred microns in lateral direction. In our experiment, a good CdZnTe detector was chosen but the deviation should still be noticeable according to Kaye et al. [33]. Therefore, we suspect material defects to be the main cause of the slight inaccuracy of the collimator experiment result. The sub-pixel position resolution of electron cloud centroid is proportional to the energy deposition. The reason is the induced signals on the neighboring pixels are proportional to the energy deposition while the electronic noise is a constant. However, with the energy deposition increases, the electron cloud size gets larger. The total influence of those two effects will make the measured gammaray interaction position resolution improve at first with energy deposition increasing and then degrade when the energy deposition passes a favorite energy. On the other hand when the energy of recoil electrons is very high, the electron track would be very long and there might be a chance to extract the electron cloud distribution and reduce the impact of the large electron cloud size on identifying gamma-ray interaction position.

6.2 Complete Charge Collection Boundary If a source is placed on the detector’s cathode side and far from the detector, the single-pixel photopeak counts should be distributed uniformly along the lateral plane of the collecting pixel. The boundary of this distribution marks the edge of the complete charge collection region. If the steering grid between the pixels is biased at the correct voltage, the electrons are expected to be steered toward the pixel and no charge should be lost in the gap between anode electrodes. In this case, the full pixel is the complete charge collection region and photopeak counts distribution should spread from one pixel edge to another, namely from .−0.86 to 0.86 mm since the pixel pitch is 1.72 mm. When the grid is unbiased or grounded, only those events located under the pixel pad can be fully collected. The complete charge collection region should shrink to the pixel pad size, which is 1.22 mm. Figure 9 shows the distribution of measured single-pixel photopeak events within a pixel when the steering grid is unbiased. The dotted line marks the measured pixel boundary of complete charge collection. As shown, the complete charge collection region is from .−0.6 to 0.6 mm, totally 1.2 mm, consistent with our expectation. The pixel boundary can affect the measured result of the collimator position. When the collimator is placed close to the complete charge collection boundary with unbiased grid, a portion of events will lose some charge to the gap or the grid and then they will not be registered as photopeak events. If we only choose photopeak events to measure the collimator center position, the measured collimator center position will be shifted. Figure 10 shows that the center position of the selected photopeak events, or the measured collimator center, is shifted toward the inside of the pixel when the collimator is placed near the edge of the complete

Sub-pixel Sensing for Pixelated CdZnTe Detectors

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Fig. 9 The distribution of single-pixel photopeak events inside a pixel

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charge collection region. The dotted line shows the edge of the complete charge collection region. A simulation was carried out to test this behavior. The result is also shown in Fig. 10. The solid curve gives the calculated collimator center using only photopeak events based on the sub-pixel calculation algorithm. It agrees well with the measurement.

7 Sub-pixel Position Sensing for Two-pixel Events Two-pixel events can be categorized into three groups according to the distance between the center of the two triggering pixels: 1. neighboring events, including side neighboring or diagonally neighboring events 2. non-neighboring events with the distance less than three pitches, and 3. non-neighboring events with the distance greater than or equal to three pitches. In the discussion above, we only considered the induced signals on the 8 pixels surrounding the charge collecting pixel. For the non-neighboring pixels, the distance to the electron cloud is far, but signals are still induced. However, these signals are so small that we can ignore them in a first order approximation. With this assumption, the sub-pixel position calculation can be performed in the same way as it was for single-pixel events in case (3). However, for case (1) and case (2), the induced signal

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Fig. 11 The two cases of the arrangement of the triggered pixels for neighboring pixel events

on a neighboring pixel from one electron cloud may be polluted by the induced signal from another electron cloud. To study these two cases, they can be further grouped into two categories based on the arrangement of the triggered pixels: (a) the two collecting pixels are diagonally placed, or diagonal-neighboring (b) the two collecting pixels are both on the same row or column, or sideneighboring Figure 11 illustrates the two categories of neighboring pixel events. In Fig. 11a, the two collecting pixels are pixel A and pixel B. The neighboring pixels of pixel A are labeled as A1, A2, A4, A5, A6, A7 and A8, while for pixel B as B1, B2, B3, B4, B5, B6, B7 and B8. Based on our assumption that the induced signals on nonneighboring pixels are negligible, the signals on the neighboring pixels except pixel B7/A5 and pixel B4/A2 are induced only by one electron cloud and their amplitudes can indicate the position of that electron cloud. These unpolluted neighbors are sufficient to apply neighbor-to-center ratio (as defined in Sect. 4) and both x and y sub-pixel positions can be determined. For the side-neighboring case shown in Fig. 11b, the x-direction unpolluted neighbors for collecting pixel A are A1, A4 and A6. They form one column so one can apply the neighbor-to-center ratio for x direction. However, for the y direction, there is not an entire row of 3 unpolluted neighbors. Therefore, the corner neighbor ratio method needs to be employed. We will discuss the application of neighbor-tocenter ratio first and then the corner-neighbor ratio. As discussed in Sect. 4, the neighbor-to-center ratio does not have a linear relationship with the interaction position. However, the opposing-neighboring ratio is a linear function of interaction position. Therefore, we can associate the neighborto-center ratio with the opposing-neighbor ratio to calibrate the nonlinear relation. This step can be done for single-pixel events. To demonstrate the effectiveness of the neighbor-to-center ratio, we again use a fan-beam collimator experiment. The collimator was placed near the center of a pixel and its opening was oriented along the y direction so that all the events through the collimator were located around x=0. The neighboring two-pixel photopeak events were chosen and the sub-pixel position of the first interaction (its electron

Sub-pixel Sensing for Pixelated CdZnTe Detectors 45

Opposing−neighboring ratio method for 2−pixel events Neighbor−to−center ratio method for 2−pixel events Opposing−neighboring ratio for 1−pixel events

40 35 30

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Fig. 12 Sub-pixel position for the two-pixel events in the collimator experiment. The energy deposition on the neighboring pixels is required to be greater than 100 keV

57

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cloud was collected by the collimated pixel) was calculated with the neighbor-tocenter ratio. As a comparison, we also blindly applied the opposing-neighboring ratio method even though the neighboring pixel signals were polluted. If the sub-pixel position calculation was correct, we should observe the first interaction position around x=0. The results are presented in Fig. 12. The sub-pixel position distribution for single-pixel photopeak events is also plotted to give a reference position of the collimator. As can be seen, the sub-pixel position calculated from the opposingneighboring ratio is pushed away from the real interaction position. Since for neighboring two-pixel events, a neighbor is collecting charge and its total induced signal becomes much higher than it should be. The neighbor-to-center ratio method gives a much better result. However, the position resolution is poorer than that for the single-pixel events. A major reason is that the energy of each interaction of a two-pixel photopeak events is less than that of single-pixel photopeak events leading to smaller induced neighboring pixel signals. Additionally, the neighborto-center ratio for neighboring two-pixel events assumes the induced signals are negligible if the distance is greater than two pixels. However, the induced signals are not exactly zero. This small charge induction can cause small offsets of the calculated interaction position from the real interaction position. This effect will be most prominent when the electronic noise becomes very low. In Fig. 11b, the y sub-pixel position needs to be calculated by the corner-neighbor ratio. As mentioned in Sect. 4, the corner-neighbor ratio is a function of both x and y coordinates. Thus, the x sub-pixel position needs to be calculated first by the centerto-neighbor ratio and then the corresponding relation of corner-neighbor ratio versus y position can be extracted and used for calculating the y sub-pixel position. As a result, the corner-neighbor ratio is expected to have higher uncertainty than the neighbor-to-center ratio. For more than two-pixel events, such as three-pixel, four-pixel or even more pixel events, as long as a unpolluted neighbor can be identified, opposing-neighboring ratio, center-to-neighbor ratio or corner-to-neighbor ratio can be used to estimate the sub-pixel location. The same algorithm discussed above can be used. However, if there is no unpolluted neighbor, this algorithm won’t able to calculate the subpixel location.

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8 Sub-pixel Position Sensing for Charge-sharing Events Charge-sharing events are usually side-neighboring events. There is an algorithm to discriminate charge-sharing side-neighboring events from Compton sideneighboring events [34]. As discussed, the sub-pixel location can be determined using center-to-neighbor ratio and corner-neighbor ratio. However, they are not accurate, especially for charge-sharing events. The electron cloud is on the gap between the collecting pixels and far away from the neighbors that can be used for neighbor-to-center ratio. The neighbor signal amplitude will be very small and the signal-to-noise ratio will very poor. In addition, the “center” amplitude needs to be the sum of the two collecting pixels. But there will be severe crosstalk between the two collecting pixels. The “center” amplitude will be altered. Therefore, the neighbor-to-center ratio will perform very poor for charge-sharing events. Since there is only one electron cloud for a charge-sharing event, there is a method to better determine the sub-pixel location of this electron cloud. One traditional method to determine the sub-pixel location for charge-sharing events is the ratio of the energy deposition between the two shared pixels. This method is called energy ratio in the later context of this paper. The energy ratio method works well when electron cloud is a consistent sphere. It is usually true when the energy is low, and diffusion dominates. However, when the energy is high, the electron cloud will have some shape. And there will be problems. First, at high energy, electron cloud size and shape are not consistent. They must be known to translate an energy ratio value into the centroid location of the cloud. Unfortunately, both electron cloud size and shape changes as a function of energy. A Geant4 [35] simulation was carried out to describe the problem. Figure 13 presents an example of the simulated energy deposition of a fast electron traveling inside a CdZnTe detector. Electron-hole pairs will generate around these energy deposition locations, which will form an electron cloud. When the energy is only 60 keV, the electron cloud is small, only about several micrometer. When the electron cloud drifts to the anode side, its size will be dominated by diffusion, whose contribution is about 50 .μm [36] for a 20 .× 20 .×15 mm.3 CdZnTe detector biased at .−3000 V. The shape of the electron cloud is close to a circle since diffusion dominates and it is isotropic. When the fast electron energy is as high as 662 keV, the electron cloud becomes much bigger, which is around 200 .μm as shown in Fig. 13c. The average electron size increases roughly linearly with energy. But the uncertainty of the size increases at the same time [4]. It is difficult to determine the size of a particle electron cloud when the energy is high. As for the shape, since the contribution from diffusion is still around 50 .μm, the 200-.μm 662-keV electron cloud will maintain its shape as generated when it reaches the anode side. Therefore, the electron cloud shape for high energy events will depend on the fast electron track. For example, the energy deposition presented in Fig. 13c could generate an electron cloud like a long spindle. The fast electron track generation is a random process. Given the energy of a fast electron, it is unpredictable what track it will produce. It makes the shape of the electron cloud at high energy undetermined. As a summary, both the size and the

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Fig. 13 Examples of the simulated energy deposition of an electron traveling inside a CdZnTe detector. Each dot gives the location of the energy deposition. The size and color give the amount of the energy deposited at that location

shape are random for high energy events. It is difficult to acquire them accurately in real applications. Second, even if the electron cloud size and shape is known, the centroid location of the cloud is still undetermined if the electron cloud is anisotropic. For example, if an electron cloud is like a long spindle, with the same energy ratio, the electron cloud centroid changes if the electron cloud orientation changes. Unfortunately, at high energy, anisotropic electron cloud is more likely. It makes it inaccurate to determine the electron cloud centroid with energy ratio for high-energy events. To obtain accurate sub-pixel location, neighbor signals must be used. Different from the charge collecting pixels, the signals induced on the neighboring-pixel are produced by the movement of the electron cloud and no charge will be collected on them. The neighboring-pixel signals are usually transient signals. Their amplitude depends on the distance between the neighboring pixel and the electron cloud [37] . A short shaper is used to pick up the amplitude of these signals. Figure 11b is used to define the signals. Here, we define: (1) far-left neighbors as the leftmost signals (B5+B8+B3) and far-right neighbors as the rightmost (A4+A6+A1); (2) adjacent-left neighbors as the two left neighbors above and below the collecting pixels (B7/A8+B2/A3) and adjacent-right neighbors as the two right neighbors (B6/A7+B1/A2); (3) adjacent-upper neighbors as the two upper neighbors (B7/A8+B6/A7) and adjacent-bottom neighbors as the lower ones (B2/A3+B1/A2); (4) the two collecting pixels are represented as B and A. The ratio of these signals can give the information of the interaction location. To keep symmetry, the ratio of a pair of signals X and Y is defined as (X.−Y)/(X+Y) in this article. Like single-pixel sub-pixel sensing, the ratio between far-left neighbors and farright neighbors should give the centroid of the electron cloud for the charge-sharing event. This far-neighbor ratio, however, has poor signal-to-noise ratio. Because of the large distance, the signal amplitude of those far-left and far-right neighbors are small. The position resolution will then be poor using the far-neighbor ratio. It is not

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Fig. 14 Normalized plot of (a) far-neighbor ratio vs. energy ratio and (b) far-neighbor ratio vs. adjacent-neighbor ratio for 662-keV 2-pixel side-neighboring events with depth separation less than 1 mm

an ideal method for charge-sharing events sub-pixel sensing. But this method can be used to determine the feasibility of other proposed algorithms. Two methods are investigated: (1) energy ratio between the collecting pixels B and A; (2) adjacent-neighbor ratio, which is the ratio between adjacent-left and adjacent-right neighbors. In Fig. 14, the relation between the energy ratio and adjacent neighbor ratio vs. far neighbor ratio are plotted respectively for 662-keV 2-pixel side-by-side neighboring events, or side-neighboring events, with depth separation less than 1 mm. The selected events are mostly charge-sharing events. Inevitably, A few same-depth Compton-scattering events will be included. Farneighbor ratio can be treated as the real location of that electron cloud for charge sharing events. As shown in the plot, when energy ratio is either close to 1 or .−1, there is no one-to-one relationship between the electron cloud centroid and the energy ratio. Depending on the electron cloud orientation, the centroid can change significantly. On the contrary, the adjacent-neighbor ratio shows a clear one-to-one relationship with the far-neighbor ratio. It is clearly more reliable to determine the electron cloud centroid for charge-sharing events. A simulation [38] is performed to understand the underline relationship between the electron cloud centroid of the charge-sharing event and adjacent-neighbor ratios [5]. Shockley-Ramo theory [28] is the basic principle used for signal induction calculation on all the electrodes. Maxwell was employed to calculate the static electric field inside the detector. Geant4 was selected to simulate the physics especially the electron cloud generation. The electric field inside the detector was assumed to be uniform. It is true that in a real detector, the electric field is not always perfectly uniform because of the material non-uniformity [39] . However, for many detectors, the electric field is close to uniform [40] . To the first-order approximation, we pick constant field to simplify the calculation. In fact, since the neighbor transient signal only happens about 1-pixel away from the anode surface [28], it is reasonable to assume uniform electric field in this region. For extremely non-uniform detectors, corrections can be made [41].

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Fig. 15 Simulation result of using adjacent-neighbor LR and UD ratio to determine x and y subpixel position, assuming the charge is shared along x direction. Plot (a) and (b) gives the 2-D and 3-D views of the adjacent-neighbor LR ratio as a function of the X position. Plot (c) and (d) gives the same views of the adjacent-neighbor UD ratio versus Y position

The result is presented in Fig. 15. It is assumed that the charge is shared along x direction as shown in Fig. 11b. The left and right column of plots give the relation between adjacent-neighbor left-to-right ratio vs x location, and adjacent-neighbor top-to-bottom ratio vs y location, respectively. Figure 15a gives the adjacentneighbor left-to-right ratio as a function of x location. Each curve is for one y location. Similarly, Fig. 15c depicts the adjacent-neighbor top-to-bottom ratio as a function of y location. Each curve is for one x location. The lower two plots are 3-dimensional view of the adjacent-neighbor ratio as the x and y location. As can be observed in those plots, the adjacent-neighbor ratio vs y location curve is independent of the x location, and it is a linear function to the first order of approximation. The neighbor transient signal amplitude was extracted independent of depth as discussed in [37]. Therefore, the linear relationship is expected for all depth. The ratio definition of the adjacent-neighbor signals removes the energy dependence. However, if the electron cloud is too large and it is shared among more than two pixels, the adjacent-neighbor ratio will not only contain the induced transient signal, but also the charge collecting signal. The linear relationship will then not be guaranteed. As for the adjacent-neighbor ratio vs x location, it depends on the y location, and it is nonlinear as shown in Fig. 15a. Therefore, to calculate the sub-pixel location based on the adjacent-neighbor ratio, one should calculate the y location first using the adjacent-neighbor top-to-bottom ratio. Then, based on the y location, one can derive the adjacent-neighbor ratio vs x location curve. The x location can be then calculated. Because of the nonlinearity, simulation is necessary to map out the relation between the location and adjacent-neighbor ratio. Based on method described above, the sub-pixel location of the two-pixel chargesharing events for a real measurement can be calculated. It can be compared to

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Fig. 16 Sub-pixel position distribution of single-pixel events and 2-pixel charge-sharing events for pixel (6,3), pixel (4,4) and pixel (3,2) using 662-keV photopeak events

the distribution of single-pixel events to validate the result. Figure 16 provides the calculated sub-pixel distribution for charge-sharing events and single-pixel events. The source is a 30-.μCi .137 Cs point source placed about 20 cm from the cathode side. The plot axis range is from .−1 to 1 mm. The actual pixel range is .−0.86 to 0.86 mm. The extra bins are for overflow events from noise and abnormal signals. Each pair of plots are for one pixel. The plots in the left column are for singlepixel events. The plots in the right column are for 2-pixel charge-sharing events. Each row presents the result for a pixel. Charge-sharing is identified by selecting side-neighboring events with depth separation less than 1 mm. There will be a few Compton-scattering events mis-classified to be charge-sharing events in the plot. But their fraction is very small and can be neglected. From the plots, we can see the distribution from the single-pixel events matches with the distribution from the charge-sharing events. For example, for pixel (6,3), there is a dent at left edge of the single-pixel distribution. For charge-sharing distribution, there is a clear hump at the inner left edge to match the dent. It is clear evidence to show the effectiveness of the sub-pixel sensing technique for charge-sharing events. The origin of such dent is so called pixel-jumping effect [33]. The incoming gamma-ray flux is uniform. However, due to material defects, some electron clouds travel along a curve instead of a straight line. The lateral movement of those electron clouds result in distortion or non-uniformity of the observed events distribution at the anode side. Figure 17 shows the flooded radiation result using 662-keV .137 Cs source for 7by-7 inner pixels in detector 6RID-5. The source is placed about 20 cm from the cathode side. The intensity of the source is about 30 .μCi. 1-pixel events and 2-pixel charge-sharing events are both plotted, as well as the sum of them. As shown, the charge-sharing events fills the gap left by 1-pixel events reasonably well. There are

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Fig. 17 Sub-pixel distribution of a flood radiation from a .137 Cs 662-keV source for 1-pixel and 2-pixel charge-sharing events in 6RID-5

several holes and many hot spots in the sum distribution. They should be due to the pixel-jumping effect discussed previously.

9 Summary The purpose of this article is to introduce and justify a sub-pixel calculation algorithm based on the digital readout of the induced signal on the charge collecting pixel and its 8 neighbors. Without such a method, the lateral position resolution of pixelated, 3-D position sensitive, CdZnTe detectors is limited by their pixel pitch. This barrier introduces a significant limitation on the Compton imaging and coded-aperture imaging performance. To improve lateral position resolution to the sub-pixel scale, algorithms based on signals induced on pixels that neighbor a charge collecting pixel are used. The opposing-neighboring ratio method is shown to be capable of providing accurate estimates of sub-pixel electron cloud centroid position. A detailed system simulation predicted 180-.μm FWHM position resolution at 662 keV with 4-keV electronic noise. A collimator experiment resulted in a 360 .μm position fluctuation for a 662 keV .137 Cs source. After subtracting the uncertainty caused by the collimator beam width and the electron cloud size, the experimental sub-pixel position resolution for measuring the electron cloud centroid of a recoil electron is found to be about 230 .μm. The uncertainty of measured gamma-ray interaction position would then be 330 .μm at 662 keV if we assume the secondary electrons are emitted isotropically. Besides the opposing-neighboring ratio, two additional methods (neighbor-tocenter ratio and corner-neighbor ratio) are discussed for the more difficult case of multi-pixel charge collection events. It is demonstrated that neighbor-to-center ratio method is effective in estimating the sub-pixel interaction position for two-pixel events. For charge-sharing events, a special algorithm is introduced to improve their subpixel resolution. Two methods are discussed: energy ratio and adjacent-neighbor ratio. The energy ratio method is not accurate for high-energy events since the electron cloud shape and the induced centroid location uncertainty due to the

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electron cloud orientation. Using adjacent-neighbor ratio, more accurate sub-pixel location can be obtained. Experimental measurement was taken and the result was shown to demonstrate the effectiveness of the method.

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Machine Learning Approaches in Room Temperature Semiconductor Detectors Srutarshi Banerjee, Miesher Rodrigues, Manuel Ballester, Alexander Hans Vija, and Aggelos K. Katsaggelos

1 Introduction RTSDs and semiconductor detectors such as HPGe are required for a large number of applications such as medical imaging, homeland security, astronomy and high energy physics [1–5]. These applications call for high quality crystals at reasonable cost, with uniform and optimized charge transport properties – no polarization effect, excellent fabrication quality, high breakdown voltage, high drift velocity, high energy resolution and lowest possible defects (charge trapping centers). Over the last several decades, RTSDs such as CdTe, CdZnTe, HgI2 , TlBr have emerged as potential detectors. RTSDs are often used as compact radiation detection units with highly segmented anode and cathode patterns. For the case of single charge carrier (electrons), the segmented anode pattern is often used, while for the significant drift of holes in the detector (along with electrons), segmented anode and cathode design is required for better energy resolution. Compared to the semiconductor detectors, RTSDs are a preferred choice today due to the high energy resolution spectral responses without the need for cooling. The performance and yield of high-quality detector-grade materials for real world

S. Banerjee () Electical and Computer Engineering, Northwestern University, Evanston, IL, USA X-Ray Science Division, Argonne National Laboratory, Lemont, IL, USA e-mail: [email protected] M. Ballester · A. K. Katsaggelos Electical and Computer Engineering, Northwestern University, Evanston, IL, USA e-mail: [email protected]; [email protected] M. Rodrigues · A. H. Vija Molecular Imaging, Siemens Medical Solutions USA Inc., Hoffman Estates, IL, USA e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_4

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applications are limited by the presence of high concentrations of defects which are randomly distributed. The manufacturing processes of the RTSD crystal is often non-uniform and this leads to random distribution of defects in the material. RTSDs such as CdZnTe (CZT) suffers from major detrimental defects [6] such as compositional inhomogeneity due to non-unity segregation coefficient of Zn [7], presence of high concentration of secondary phases, Te inclusions and sub-grain boundaries/dislocation walls in high concentration in CZT array. These defects act as trapping centers, hindering localized charge transport and imposes spatial nonuniformity in charge transport properties, thereby adversely affecting the detector performance [8–13]. The trapping centers have lower ionization energies than the bandgap of the material and enables transition of charged carriers (electrons or holes) from the valence band or conduction band. These trapping centers can be non-uniform over the volume of the material and typically differs for electrons and holes. The efforts to characterize these detectors have been done over the last several years. For instance, using thermoelectric emission spectroscopy (TES) and thermally stimulated conductivity (TSC) measurements, the thermal ionization energies of the electron and hole traps were measured [14]. Determination of the trap lifetime was done using a microwave cavity perturbation method in CdZnTe and HgI2 [15]. In [16], the electron and hole traps of CdZnTe samples were radially irradiated with 5 MeV focused proton beam to generate electron-hole pairs and fill traps, which were released later by thermal re-emission. Electron and hole traps were distinguished by excitation near the vicinity of the appropriate electrodes. Analyzing simultaneous multiple peaks on TSC measurements allowed characterization of deep trap levels in CdZnTe [17]. In [18], the average hole trapping time τ h was derived using statistical model of charge collection efficiency based on known electron average trapping time. In [19–21], average hole detrapping time τ Dh was extracted by comparing the measured and simulated signals for holes as measured in the cathode. Imperfections due to mechanical damage or adsorbed chemical species trap charges or increase leakage current. Using pulsed laser microwave cavity perturbation method selectively at the surface and in the bulk region of CZT, these defects has been characterized [22]. The influence of type of metal contacts and deposition techniques on the recombination and trapping defects at the metal-semiconductor interface has also been studied [23]. The uniformity of high flux CdZnTe has also been characterized [13]. In literature, the defects and charge transport properties of electrons and holes are measured using classical approaches considering homogeneous behavior over the detector. This requires cumbersome multiple experiments and technical know-how. However, the homogeneity and repeatability of the defects and charge transport properties within a detector and across multiple detectors spatially and temporally are unknown. Moreover, achieving high energy resolution below 1.0% at 662 keV and submillimeter position detection accuracy depends on in-depth characterization of the RTSDs. Detailed electrical and material characterization of RTSD will also aid in developing improved reconstruction algorithms. However, this approach traditionally is hugely time consuming, requires numerous sophisticated experiments and

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skilled manpower. On the other hand, deployment of such detector arrays requires precise characterization of the individual detectors, and knowledge of the defects within the sensors spatially and temporally. Sensors with defects are typically discarded, which significantly reduces manufacturing yield, increases production cost and results in financial loss. In order to solve this important problem, we utilize a Machine Learning approach. Machine learning and deep learning-based models have not only been popular in the last few years but also have created a paradigm shift in different fields such as material science, drug discovery and others. Integrating Physics-based Modeling and Machine Learning is becoming more popular over the years [24, 25]. The overall objectives of such approaches are to develop inverse models, improve predictions beyond state-of-art physical models, model parameterization, partial differential equations (PDEs) solutions, discover symbolic governing equations, and others. Solving problems in physics governed by PDEs using Neural Networks has been done [26, 27]. For example, the two-dimensional wave equation is modeled as a Recurrent Neural Network [28]. DeepONets [29] have been demonstrated as a powerful tool to learn nonlinear operators in a supervised data-driven manner. The 2D Poisson Equation has been solved with a Physics Informed Neural Networks [30]. In most of these physics-based machine learning approaches, relatively simpler PDEs have been solved. However, the charge transport in a RTSD has multitude of coupled PDEs [31] involving charge drift, trapping, detrapping and recombination. To the best of our knowledge, our work is the first novel approach to characterize the radiation detectors using machine learning. In our machine learning based physical models [32–36] we solve the following problems currently plaguing the characterization of radiation detectors with a reasonable detection area for its wide scale implementation in medical and security applications: (a) Micron-level characterization of detector material properties with spatial and temporal uniformity in a fast and efficient way, (b) Determination of detector material properties as per industry standards, (c) Determination of detector material properties based on reduced amount of data, and, (d) Micron-level defect identification and characterization.

2 Classical Approach to Detector Modeling In solid-state detectors, depending on the end application, electrons and holes transport properties play a significant role in selecting detectors. Compensation techniques used to increase the resistivity of RTSDs with mostly shallow defect levels introduce deep defect levels in them [37]. The deeper defects degrade the performance of the RTSDs owing to longer trapping centers for charges. The trapping, detrapping and recombination is governed by Shockley-Read-Hall Theory [38, 39]. Rodrigues et al. [40] worked on techniques to measure more detailed properties of these materials using the charge transport equations driven by the charge continuity equations with multiple electron and hole defect levels – trapping

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Fig. 1 Energy level diagram of a RTSD showing shallow electron trapping centers along with shallow and deep hole trapping centers, (i) Before photon interaction; (ii) Electrons-holes in excess of equilibrium generated at t = 0; (iii) Transport of electrons and holes by operating electric field alongwith trapping, de-trapping, and, recombination for t > 0. (Figure adapted with permission [32])

centers – coupled with Poisson’s equation [41–44]. The macroscopic equations in [31] describe the various phenomena occurring in the material when photons, Xrays or energetic gamma rays interact with the material usually by Photoelectric, Compton or Pair-Production type of interaction, creating electron-hole pairs. Once the electron-hole pairs are created the following phenomena occur: (1) drift of charges (electrons and holes) due to electric field between the electrodes, (2) free charges getting trapped and de-trapped in defect levels within the material, (3) recombination of free charges, which are modeled as capture of free electrons followed by capture of free holes in the material [45] (Fig. 1). Equation (1) describes the electron movement in the RTSD. The dynamic concentration of free electrons is ne in excess of equilibrium. There is an increase in electron concentration at a spatial region due to charge creation in the bulk, drift of charges to that region and de-trapping from trapped levels. On the other hand, there is reduction of charges in the same region due to diffusion, trapping, and recombination of charges. The model considers that the trapped charges never saturate the trapping centers, since excess carrier concentrations are small compared to the number of available trapping and recombination centers and the simplified equations can be used [41]. In Eq. (1), only 1 trapping level for electrons has been shown, while in principle there can be several trapping levels, .

∂ne ne n˜ e1 ne + ∇· (ne μe ∇φ) = − − + + · · · + δe , τe τeT 1 τeD1 ∂t

(1)

where μe is the mobility of the electrons, φ is the voltage, τ e is the electron lifetime, n˜ e1 , τ eT1 , and τ eD1 are respectively the concentration, trapping, and detrapping lifetime of electrons in trapped level 1, δ e is the source term. The increase in concentration of electrons in trapped level 1 is dependent on its own concentration .n˜ e1 , concentration of free electrons ne , trapping and detrapping lifetimes τ eT1 and τ eD1 respectively, as shown in Eq. (2),

.

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ne ∂ n˜ e1 n˜ e1 = − . τeT 1 τeD1 ∂t

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(2)

A similar equation applies to holes, as shown in Eqs. (3) and (4) considering 2 trapping centers for holes and recombination of electrons and holes. Equation (4) shows the increase in holes trapped in trapping centers 1 and 2, .

∂nh nh nh n˜ h1 nh n˜ h2 + ∇· (nh μh ∇φ) = − − + − + + · · · + δh , ∂t τh τhT 1 τhD1 τhT 2 τhD2 (3)

.

nh nh ∂ n˜ h1 n˜ h1 ∂ n˜ h2 n˜ h2 = = − , − , ∂t τhT 1 τhD1 ∂t τhT 2 τhD2

(4)

where nh is the dynamic concentration of free holes in excess of equilibrium. μh is the mobility of the holes, and τ h is the hole lifetime. .n˜ h1 , τ hT1 , and τ eD1 are the concentration, trapping, and detrapping lifetime of holes in trapped level 1 respectively. Similarly, .n˜ h2 , τ hT2 , and τ hD2 are the concentration, trapping, and detrapping lifetime of holes in trapped level 2 respectively. δ h is the source term. The drift of charges is dependent on the electric field E, as shown in Eq. (5), with the voltage satisfying the Poisson equation Eq. (6), E = −∇φ,

.

∇ 2 φ = −k

.

q (ne + n˜ e1 + nh + n˜ h1 + n˜ h2 + · · · ) . 

(5)

(6)

where  represents the permittivity of the RTSD material in Eq. (6). The temporal dynamics of free electrons and holes following the SRH model is affected by the trapping energy states in the bandgap [46]. For free hole concentration p, with trapping and detrapping lifetimes τ Ti and τ Di respectively for ith trap, and pti as the concentration of holes in the ith trap, the following equation can be written [46],   p dp  pti . − = + . τT 1 τDi dt

(7)

i

The trapping and detrapping lifetimes dictate whether the defects induce short term or long-term trapping of charges in the detector. Considering the low probability of transition of charges between the trapping centers, the occurrence of such process [47] is neglected in Eq. (7). Signals collected at the electrodes arise due to the movement of charges [48–51]. High energy photons (γ -rays or X-rays) are incident on the detector and creates electron-hole pairs. The hole drifts towards the cathode and electrons towards the

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Fig. 2 (i) Incoming high energy photons (γ -rays or X-rays) interacting with the detector having pixelated anode and a single cathode; (ii) Electron-hole motion in the detector – (a) Sensor pixelated anode pattern, (b) Central region model illustrating pixelated anode design with uniform material and electrons-holes drift in bulk. (Figure adapted with permission [32])

Fig. 3 (i) Electric field profiles for simulated materials A and B, (ii) Anode Signals C, CAT and NE simulated for materials A and B (for electron-hole charge injection at Voxel 50). (Figure adapted with permission [32])

pixelated anodes as shown in Fig. 2a. The detector setup is shown in Fig. 2b(i, ii) with the 9 grid electrodes on the anode side (NW, N, NE, W, C, E, SW, S, SE) and 1 single large cathode electrode (CAT). Since the mobility of electrons is higher than holes, only single cathode is used, and grid anodes are used. In case hole mobility is also significant, grid cathode can also be used. Figure 3(i) shows 2 cases of the electric field – uniform and piece-wise linear which are plausible inside the RTSD, while Fig. 3(ii) shows the signals observed in the cathode electrode and three adjacent anodes (center or collecting anode, north and north-east or neighbors)

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for electron-hole pair injection at voxel position 50, where in this case the cathode was at position 0 and anode at position 100. At a quick glance, there is almost no difference in the signals generated at the electrodes due to the 2 Electric Fields as shown in Fig. 3(ii). However, with a closer look at the electric field profiles in Fig. 3(i), we can see distinct differences between them. Our learning-based approach can clearly distinguish between these two electric field profiles as shown in Fig. 3(i) from the signals shown in Fig. 3(ii), along with the charges transport in the volume of the RTSD. The data for training the proposed learning model has been generated using the classical equations, Eqs. (1), (2), (3), (4), (5), (6) and (7). A code based on these equations has been developed to define the charge transport equations in the detector, by defining the trapping, de-trapping and recombination lifetimes of electrons and holes as constant pre-defined parameters, with varying the electric field along the material. This classical model has been created by spatially discretizing the detector. For a charge input at a voxel position, the signals are generated in the cathode and pixelated anode. Additionally, the free and trapped charges in different spatial pixel locations are computed. These signals, free and trapped charges are computed for each time step, with the total number of time steps defined a priori. The input-output data for training the learning-based model consists of the input electron-hole pair injected at a known voxel position and the output as the signals, free and trapped charges in different spatial voxels of the classical model over different time steps.

3 Machine Learning Based Full Model of Detector We introduce a novel method to determine the material properties such as μe, h , τ eT1 , τ eD1 , τ hT1 , τ hD1 and recombination coefficients of free and trapped electrons and holes at spatially discretized locations in the RTSD. The detector is subdivided into N voxels, where the division can be in a 1D, 2D, or 3D manner. In each of the discretized volume (or voxel) i, the RTSD properties such as μe, h, i , τ eT1, i , τ eD1, i , τ hT1, i , τ hD1, i are defined. These weights are thus spatially discrete from each other. For instance, the mobility μe is converted into N discrete values of wTrpt, e . Now, the relation between μe and μh can be separately modeled as unknowns or be related to each other. This physics-based learning model therefore allows the determination of each of these unknowns in the RTSD. For each of these coefficients (referred here as τ in general), we compute the number of charges particles (electrons or holes) t − remaining in that particular level as .Nlef t = N0 e τ , where N0 and Nleft are the number of charged particles at a particular level at t = 0 and at time t respectively. Thus, given the time t = t1 , (example, t1 = 10 ns for the 100-voxel model) and given τ , we can compute the fraction of charges transitioning from an energy level to another and those remaining in the same energy level.

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Fig. 4 RTSD model with (i) 1D voxels and electrodes, and (ii) Overview of the learning-based physical model of RTSD. The model consists of trainable weights in each voxel. The charges move dynamically from one voxel to another based on the Electric Field and polarity (blue for electrons, and red for holes). The free and trapped charges in each voxel with the signals generated during movement of charges are used as output of the model. Cathode and Anode is on outer ends of Voxel 1 and N respectively. (Figure adapted with permission [33])

3.1 Machine Learning Based Physical Model A voxelated representation of the detector in 1 dimension is shown in Fig. 4(i). Linearly the material is divided into N voxel segments with the electrodes at either end, anode on the right and cathode on the left. We consider a grid anode with M electrodes (M = 9 for illustration) and a single cathode. The high energy photons can interact in any position in the detector. The resultant physical model in turn is a discretized version of the physical phenomena occurring in the RTSD over time. The model can be thought of as being analogous to a network composed of Long Short Term Memory (LSTM) or Gated Recurrent Unit (GRU) cells [52]. However, in a LSTM/GRU model it would require more weights. This will lead to not only training the model with more weights and with more training data and time. In order to remove these limitations, we introduce a model which corresponds to the exact physics-based equations as shown in Fig. 5(i). In Fig. 5(i), the operations taking place in voxel i at time t are shown. At a time t − 1, the charge in voxel i in free state is .qht−1,i for holes and .qet−1,i for electrons. Under the influence of Electric Field, holes drift at time t from other voxels i + 1, t,i+1 t,i+k t,N · · · , i + k, · · · N, to voxel i, with charges .qh,o , · · · , qh,o , · · · , qh,o respectively. These charges are added into the existing charge .qnt−1,i to form the total charge due t,i to holes in voxel i at time t, referred here as .qh,int . The subscript int refer to the total or integrated charge due to sum of all holes in voxel i at time t. Some of the holes recombine with the intrinsic electron concentration in the bulk of the material with t,i weight whRec, i , which in voxel i at time t is referred as .qh,Rec . The subscript Rec refers to recombination. The presence of trapped hole centers in the material traps some of the holes and detraps holes back as excess hole concentration over bulk, as

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Fig. 5 (i) Operations at voxel 3 at a particular time t. The electron transport from cathode to anode (left to right) is shown in the bottom half of this figure, while the hole transport in the opposite direction is shown in the top half of the figure and (ii) Current generation in the RTSD. For simplification, we show the 1D model with only five voxels. Charge transfer from one voxel to another induces a potential difference w at the electrodes. The product of transferred charge with w gives the generated current at the electrodes. (Figure adapted with permission [32, 33])

indicated respectively by the trapping and detrapping weights whT, j, i and whD, j, i , for hole trapping level j in voxel i. The total holes which are available for transport t,i in the valence band of voxel i at time t is termed as mobile or free holes, .qh,mob , and mob in the subscript denotes the mobile holes. In Fig. 5(i), we show just one level of trapping centers (for both electrons and holes). However, in principle, depending on the material properties there can be several trapping centers. A fraction of holes t,i wh, i drift out of voxel i as .qh,o , while the remaining holes are left behind in voxel i as .qht,i at time t. Same operations are repeated for electrons, as shown in the bottom half of Fig. 5(i). The stepwise computations for holes in voxel i are shown in Eqs. 8, 9, 10 and 11.   t,i t−1,i t,i+1 t,i+k t,N .q = q + q + · · · + q + · · · + q (8) h h,o h,o h,o h,int t,i t,i qh,Rec = whRec,i × qh,int

.

  t,i t,i qh,mob = qh,int × 1 − whRec,i − whT ,j,i + q˜h,j,i × whD,j,i

.

t,i t,i qh,o = wh,i × qh,mob

.

(9)

(10)

(11)

Figure 5(ii) shows the model with the detector discretized into 5 voxels (for explanation purposes only). The high energy rays are incident on Voxel V3 creating electron-hole pairs. The electrons drift towards the anode (right of Voxel V5), while the holes drift towards the cathode (left of Voxel V1). While drifting, the electron

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charges are multiplied by difference of potentials, shown as wL, e1 and wL, e2 for electrons drifting between voxel V3 and V4, and, V4 and V5, respectively, to generate electrical signals for electrons (signalelectrons ). Similarly electrical signals are generated due to drift of holes (signalholes ). The electrical signals are generated in the electrodes based on the Shockley-Ramo Theorem [49]. In each voxel, the free and trapped charges, as well as the signals generated at the electrodes are recorded. We also consider the voltages at the electrodes at the ends of the detector to be fixed Vi and Vf , increasing from cathode to anode in a linear manner. We consider Voxel 0 with reference position x0 , and successive Voxels 1, 2, · · · , 5, (denoted by V1 , V2 , · · · , V5 ) at positions x1 , x2 , · · · , x5 with each successive voxel at distance dx, (for example, x5 − x4 = x4 − x3 = dx) from the previous voxel. In between the 2 voxels (for example voxels 3 and 4), we can apply Eqs. 12a and 12b, where voltages V3 and V4 are linearly related. Similarly for voxels 4 and 5, we can apply Eqs. 13a and 13b, where Voltage .V4 and .V5 are linearly related. In these equations, C31 , C32 , C41 , C42 are learnable coefficients. Now, the voltage V4 and .V4 from Eq. 12b and Eq. 13a must match. Thus combining we can formulate an error term, errorvoltage as the difference between V4 and .V4 normalized over the distance of Voxel 4 from origin 0, x4 , defined in Eq. 14, .

V3 = C31 x3 + C32

(12a)

.

V4 = C31 x4 + C32

(12b)

.

V4 = C41 x4 + C42

(13a)

V5 = C41 x5 + C42

(13b)

.

error voltage = (C31 − C41 ) −

.

(C42 − C32 ) 4dx

(14)

The model is trained with input-output data pairs. The input data is the position of injected electron-hole pair along with the fraction of charge generated in that voxel. The magnitude of the injected charges is normalized to 1. The output data are the signals obtained at the electrodes along with the electrons and holes (free and trapped) in each of the voxels over time. During training of the model, the loss function is computed as the sum of the squared errors between the signals at the electrodes and charges in the voxels compared to the ground truth signals along with the .error 2voltage . The overall loss function (LF) for this model is shown in Eq. 15. The loss function in Eq. 15 is shown for simulation experiments considering CZT detector with 2 trapping centers for holes and 1 trapping center for electrons [14, 31]. However, in general, there can be several trapping centers for both electrons and holes, and thus several such terms, whose number is pre-defined, and the learningbased model needs to be designed accordingly. In the loss function, the errors due to

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the signals and voltage are grouped together, free and trapped electron charges are grouped together, and free and trapped charges due to holes are grouped together with weighting terms k, l and n respectively. The higher the value of the parameters k, l and/or n, the lower the errors associated with those terms. In these error terms, the subscript gt for a particular parameter X (for instance X is signal or qe ) refers to the ground truth data for that parameter X generated using the classical model as described and the subscript L for the same parameter X refers to the data generated by the learning-based model. 

 2 signal gt − signal L + error 2voltage

 2  2  + l qe,gt − qe,L + qet,gt − qet,L

 2  2  2  + n qh,gt − qh,L + qhT1 ,gt − qhT1 ,L + qhT2 ,gt − qhT2 ,L

LF = k .

(15) The trainable model weights are initialized to a value. Based on the electron-hole pair input to this model, the output (signals, free and trapped charges) is computed over time. The model consists of training and testing phases. In the training phase, the loss is computed using Eq. 15 for every electron-hole input pair based on the outputs from this model and the ground truth output data over time. Since our model is a recurrent network structure over time, Backpropagation through Time (BPTT) [53, 54] is used to compute the gradients of the loss with respect to the trainable (or tunable) weights of the model. BPTT unfolds the learnable model in time by creating several copies of the model which can be treated as a feed forward deep network with tied weights. The update of the trainable weights is based on a stochastic gradient descent method – ADAM optimization [55], which is based on adaptive estimation of first- and second-order moments. ADAM optimizer is used with a learning rate of 5 × 10−4 with two momentum terms set as β 1 = 0.9 and β 2 = 0.999. Learning rate higher than 5 × 10−4 causes oscillations in the loss function, while a lower learning rate slows down convergence. In each epoch (iteration), the ADAM optimization updates the trainable weights of the model based on the gradients, with the goal to minimize the loss function over the epochs. This learning-based physical model is developed using Tensorflow library [56] in Python. Over the epochs, the weights of the model such as electron transport weights wTrpt, e, i , electron trapping weights weT, i , electron detrapping weights weD, i and other weights in voxel i as shown in Fig. 5(i) in the learning-model are trained. Once the model is trained, the model can be tested based on the electron-hole pair input at voxel position. The injection position is different from the ones used for training the model. In the testing phase, there is no computation of loss. Only the signals and charges are obtained in each time step as output from the model.

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3.2 Experimental Studies In order to train and test the model actual measured data would be needed. Unfortunately, no such dataset is available in the literature for RTSD. We generate synthetic data using the classical model. Since the learning-based model is developed in a voxelated manner, the training data generated using the classical approach is also voxelated. During the training process, the loss is monitored over epochs and allowed to converge to less than 0.005 or until it stops decreasing. In our simulation experiments, there is no significant improvement in the model coefficients/weights below this threshold loss value.

3.2.1

Numerical Experiment with Unweighted Loss Function

We performed experimental studies with k = l = n = 1 in Eq. 15 and a model with 100 voxels. The voxel at one end, voxel 100 is connected to the anode terminal while the voxel at the other end, voxel 0 is connected to the cathode terminal. The material is considered as 1D and discretized into 100 equal partitions, termed as voxels for generalization, and the experiments are done with timesteps of 10 ns resolution. The simulated detector has size of 10 mm, with total simulation time of 2 μ s. The overall loss function reduces over epochs. Unit charge in terms of an electron-hole pair is injected at voxel positions 20, 30, 40, and 50. Figure 6(i–iii) show the drift coefficients, electron coefficients and hole coefficients, respectively. The drift coefficients follow the ground truth closely as shown in Fig. 6(i). It is seen in Fig. 6(iii) that hole coefficients (for trapping centers 1 and 2 and recombination coefficients) also follow closely the ground truth coefficients. There are slight oscillations near the injection points of the electronhole pair, which are mostly due to the learning of the hole coefficients for voxels less than 10 voxels away which is the length of the injection intervals of the e-h pairs. Clearly, the closer the injection points, the lower the oscillations in the hole coefficients. However, it is seen that the electron coefficients (Fig. 6(ii)) oscillate around the ground truth values for the recombination coefficients.

3.2.2

Numerical Experiment with Weighted Loss Function

We performed experimental studies with k, l, n ∈ {0.1, 1.0, 10.0, 100.0} in Eq. 15 using the 100 voxel size model. Now k, l, n can take any finite values. However, in the experimental studies, k, l, n are chosen to be linear in logarithmic scale from 0.1 to 100, which spans a wide range. The experimental data and the model size used for learning the model consists of transport, trapping and detrapping centers for electrons and holes, along with recombination of charges. We find that for k = 0.1, l = 100 and n = 100, the Normalized Mean Square Error (NMSE) [32] has a

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Fig. 6 (i) Drift coefficients (μe ), (ii) electron coefficients (weT, 1 , weD, 1 , weRec ), and, (iii) hole coefficients (whT, 1 , whD, 1 , whT, 2 , whD, 2 , whRec ) for e-h injection at Voxels 20, 30, 40 and 50. (Figure adapted with permission [32])

Fig. 7 (i) Drift coefficients (μe ), (ii) electron coefficients (weT, 1 , weD, 1 , weRec ), and, (iii) hole coefficients (whT, 1 , whD, 1 , whT, 2 , whD, 2 , whRec ) for e-h injection at Voxels 20, 30, 40 and 50 with k = 0.1, l = 100, n = 100 in Eq. 15. (Figure adapted with permission [32])

minimum of 0.1761. This combination of k, l, n values in the learning model is used for injecting charges at multiple voxel positions of 20, 30, 40, 50. Figure 7(i–iii) shows the drift, electron, and hole coefficients, respectively, for material B (material B has non-uniform electric field profile as shown in Fig. 3(i)). The weighted model prioritizes signals at the electrodes, charges (free and trapped) due to electrons and holes differently than the unweighted model. Now, since these hole and electron charges are more fundamental and the signals are generated only due to charge motion, the higher weightage of charges (free and trapped) in the loss function compared to the signals drives the model to its optimized material parameters better than the unweighted model. In both cases, e-h injection is at the same voxel locations of 20, 30, 40, 50. Clearly, choosing appropriately the regularization parameters in the loss function improved the accuracy in the learned parameters. The physical model can be designed with voxels other than 100 voxels as well. For a material with the same dimension as before, increasing the number of voxels in the model will reduce the size of each voxel. The decrease in voxel size in the model will improve the response characteristics of the output signals.

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Numerical Experiment with Model Having Higher Voxels

This model has been designed with 200 voxels having a time step of 5 ns in the ground truth model. This time step has been chosen in order to ensure that the electrons have enough time to travel from one voxel to the next adjacent voxel. For a material with the same dimension as before, increasing the number of voxels in the model will decrease each voxel size and improve the response characteristics of the output signals. The results of this model injected with electron-hole pair at voxels 80, 120 and 160 is shown in Figs. 8 and 9 respectively. The model is trained for 60 voxels at a time for electrons and 20 for holes. k = 0.1, l = 100 and n = 100 have been used in this model. Clearly for the electrons and holes, the learned coefficients of drift, trapping, detrapping, and recombination match the ground truth values for

Fig. 8 (i) Drift coefficients (μe ), (ii) electron coefficients (weT, 1 , weD, 1 , weRec ), and, (iii) hole coefficients (whT, 1 , whD, 1 , whT, 2 , whD, 2 , whRec ) for e-h injection at Voxels 80, 120 and 160 with k = 0.1, l = 100, n = 100 in Eq. 15. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [32])

Fig. 9 (i) Electron recombination coefficients (weRec ), and, (ii) Hole recombination coefficients (whRec ), for multiple e-h injections at Voxel 80, 120 and 160 with k = 0.1, l = 100, n = 100 in Eq. 15. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [32])

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the classical model for most of the cases. Different initializations for the model weights than the 100 voxels model provides better convergence to the ground truth. In this section, we describe our physics-based learning model for 100 and 200 voxels. However, this approach can be extended to any voxels as long as the physical electron and hole charge transport laws in each voxel holds true.

4 Machine Learning Based Full Model of Detector The learning-based full model of the detector uses a loss function taking into consideration the complete data as required by the classical physical equations – signals, voltage distribution in the material, free and trapped charges. In the real world, each of these data must be obtained from experimental hardware setups with the detector, which not only requires costly equipments, but also skilled manpower and time. In order to address this issue, in this section, we propose learning-based models to learn from fewer data than in the full model (which is dictated by the classical physical model). We explore the models by training with fewer data than what is dictated by the classical physical equations, step-wise removing small fraction of relevant data from the full learning-model (such as charge trapped and trapping centers) and evaluate the performance of the new physics based learning model.

4.1 Machine Learning Based Physical Model with Reduced Data 4.1.1

Physical Model-1

The Physical Model-1 has been developed using signals at the electrodes, voltage distribution along the detector, free electron charges and, free and trapped hole charges in one trap center as shown in Eq. 16. We use hole charges corresponding to only one trapping center and no electron charges for its trapping center for CdZnTe detector with 2 trapping centers for holes and 1 trapping center for electrons. Our model as shown in Figs. 4 and 5 can be trained using charges corresponding to any one of the hole trapping centers, shallow or deep. However, for illustration purposes, we have used data from shallow hole trapping center. For any other material with NTh trapping centers for holes and NTe trapping centers for electrons, we would use the data corresponding to NTe − 1 trapped charges for electrons and NTh − 1 trapped charges for holes.

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 2 2  signal gt − signal L + error 2voltage + l qe,gt − qe,L

 2  2  + n qh,gt − qh,L + qhT1 ,gt − qhT1 ,L

LF 1 =k .

(16)

The learning-based model uses the same hyperparameters k, l, n in the loss function in Eq. 15 which was derived through optimization in our last section of the chapter.

4.1.2

Physical Model-2

In Physical Model-1, we observed from our simulation experiments that the hyperparameters k, l, n in the loss function are biased heavily towards the hyperparameters l, n are much higher than k. Thus, the Physical Model-2 has been developed considering only the free electron charges and, free and trapped hole charges – in this case using hole charges in hole trapping center – 1 (for illustration purposes). The loss function LF2 is then defined in Eq. 17, LF 2 = l

.



 2  2  2  + n qh,gt − qh,L + qhT1 ,gt − qhT1 ,L qe,gt − qe,L

(17)

In general, for NTh trapping centers for holes and NTe trapping centers for electrons, we can use the free hole and electron charges, as well as electron and hole trapped charges for NTe − 1 and NTh − 1 trapping centers respectively in training the model.

4.1.3

Physical Model-3

In the Physical Model-3, we further reduce the dependency on any of the trapped hole charges which were used in the Physical Model-2, and this results in a model which characterizes the trapping centers in an equivalent manner. The equivalent trapping and detrapping lifetimes are the contribution of several trapping and detrapping lifetimes in the detector which contributes to the dynamics of charge motion in the detector as shown in Eq. 7. The properties of the physical detector can be attributed as defect-free properties in addition to equivalent defects in the material. The presence of multiple trapping and detrapping levels can be converted to equivalent trapping and detrapping levels. In such a scenario, for 2 hole trapping centers of CZT with trapping lifetimes τ 1 and τ 2 , the equivalent trapping lifetime is given in Eq. 18, .

1 1 1 = + τeq τ1 τ2

(18)

Considering the probability of trapping 1 level as .pτ1 and detrapping 1 lifetime as τdt1 , alongwith probability of trapping 2 level as .pτ2 and detrapping 2 lifetime as .τdt2 , we can calculate the equivalent detrapping lifetime as in Eq. 19, .

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Fig. 10 Equivalent Operations in Voxel i at time t. (Figure adapted with permission [33])

.

pτeq τeq

=

pτ1 pτ + 2. τdt1 τdt2

(19)

The physical model-3 is designed as a combination of defect-free model and model with equivalent defects. The equivalent computations in a voxel i is shown in Fig. 10. The equivalent trapping and detrapping weights are .whTeq ,i and .whDeq ,i for holes, and similarly for electrons, the corresponding trapping and detrapping weights are .weTeq ,i and .weDeq ,i . The charges in equivalent trap center are .q ˜heq ,i and .q˜eeq ,i for holes and electrons respectively. The loss function consists of only the free electron and free hole charges to train the model, as shown in Eq. 20, LF 3 = l

.

4.1.4



 2  2  + n qh,gt − qh,L . qe,gt − qe,L

(20)

Physical Model-4

In Physical Model-4, we use only the signals generated at the cathode and anodes due to motion of the charged particles to train. Typically, the signals are generated at the electrodes by the superposition of signals generated individually due to transport of electrons and transport of holes. However, in Physical Model-4, we separate out the signals generated due to the drift of electrons from the signals generated due to the drift of holes and then train the model. The loss function for training the physical model-4 is shown in Eq. 21,

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LF 4 =

.

 2   2  + sg h,gt − sg h,L sg e,gt − sg e,L

(21)

It is also observed from our simulation experiments that by using the loss function in Eq. 21 leads to the trained model weights which fail to converge to the ground truth solution. The solution converges to a local minimum which is different from global minimum, and hence the trained weights differ from the ground truth weights. We use a Total Variation (T.V.) regularization on the different weights of the model to converge the learned solution to the global minimum solution as observed in our simulation experiments. The loss function gets modified to LF4, m as shown in Eq. 22, LF 4,m = .

 2  + λ1 ∇weTeq + ∇weDeq + ∇we,Rec 2 sg e,gt − sg e,L

 2  + λ2 ∇whTeq + ∇whDeq + ∇wh,Rec 2 + sg h,gt − sg h,L

(22)

The T.V. regularization ensures smoothness in the trained weights of the model. The optimal values of λ1 and λ2 are determined through simulation experiments by finding the minimum error between the ground truth weights and the trained weights. The trained weights for the different Physical Models have been evaluated by computing an error metric for each of the weights. For example, for electron trapping weight (weT ) with weT, gt and weT, lr as the ground truth and trained weights respectively, the error is expressed as,

   .Err (weT ) = 

Nf in   weT ,lr,i − weT ,gt,i 2 1 weT ,gt,i Nf in − Ninj + 1

(23)

i=Ninj

The error is computed over the injection positions of the electrons/holes and the number of voxels over which the weight gets trained over the epochs. The difference between the trained weights and ground truth weights for the trained region is normalized by the ground truth weights, to take into account the different ranges of weights in the model and put equal emphasis on the different model weights. The relative error, expressed as  Nf in    weT ,lr,i − weT ,gt,i  1   × 100 .Err2 (weT ) =   Nf in − Ninj + 1 weT ,gt,i

(24)

i=Ninj

for each of the trained weight are also shown for electrons and holes for the four different physical models. For electron and hole weights, the mean of the different electron and hole weights are computed as the relative error metric.

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Fig. 11 (i) Drift coefficients (μe ), (ii) electron coefficients (weT , weD , weRec ), and, (iii) hole coefficients (whT, 1 , whD, 1 , whT, 2 , whD, 2 , whRec ) for e-h injection at voxel positions 9 with stride of 5 voxels until voxel 59 for k, l, n in Physical Model-1 as shown in the plot legend. Rec in the legend refers to recombination coefficients. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [33])

4.2 Experimental Studies 4.2.1

Numerical Experiments with Physical Model-1

We performed experimental studies with unit electron-hole charge pair injections at voxel positions 9 with stride of 5 voxels until voxel 59. The trained weights of the model for electron drift coefficients, electron and hole trapping coefficients are shown in Fig. 11(i–iii) respectively for different k, l and n in the loss function shown in Eq. 16. The error for the electron coefficients is computed from Voxels 9 to 99 since the electrons move towards anode, Voxel 100, and the coefficients in those voxels gets trained, while for the hole coefficients, the error is computed from Voxels 1–59, where the hole move towards cathode, Voxel 0. For k = 1, l = 104 and n = 103 , the mean error (Err) of the trained weights has a minimum of 0.0821, while for k = 1, l = 103 and n = 103 , the mean error (Err) is 0.1140.

4.2.2

Numerical Experiments with Physical Model-2

Unit charge in terms of electron-hole pair injections at voxel positions 9 with stride of 5 voxels until voxel 5 9 is fed into the model in order to train the model. The trained weights of the model – drift coefficients, electron coefficients and hole coefficients are shown in Fig. 12(i–iii) respectively. In the weighted loss function of Eq. 17, we use the weights l = 10, n = 1. The error values of drift coefficients (μe ), trapping (weT ), detrapping (weD ), recombination coefficients (weRec ) for electrons are 1.6108 × 10−4 , 0.1241, 0.0240, 0.1673 respectively which are computed for voxels 9 to 99. Similarly, the error values of the trapping 1 (whT, 1 ), detrapping 1 (whD, 1 ), trapping 2 (whT, 2 ), detrapping 2 (whD, 2 ) and recombination coefficients (whRec ) for holes are 0.0768, 0.0447, 0.1005, 0.0640, 0.2406 respectively which are computed for voxels 1–59. The arithmetic mean of the error of these coefficients is 0.0936.

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Fig. 12 (i) Drift coefficients (μe ), (ii) electron coefficients (weT , weD , weRec ), and, (iii) hole coefficients (whT, 1 , whD, 1 , whT, 2 , whD, 2 , whRec ) for e-h injection at voxel positions 9 with stride of 5 voxels until voxel 59 for k, l, n in Physical Model-2 as shown in the plot legend. Rec in the legend refers to recombination coefficients. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [33])

Fig. 13 (i) Drift coefficients (μe ), (ii) electron coefficients (weT , weD , weRec ), and, (iii) hole coefficients (whT, 1 , whD, 1 , whT, 2 , whD, 2 , whRec ) for e-h injection at voxel positions 9 with stride of 5 voxels until voxel 59 for k, l, n in Physical Model-3 as shown in the plot legend. Rec in the legend refers to recombination coefficients. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [33])

4.2.3

Numerical Experiments with Physical Model-3

The electron-hole charge pairs are injected at voxel positions 9 with stride of 5 voxels until voxel 59 during training the Physical Model-3 as well. The learned physical properties of the model – drift coefficients, electron coefficients and hole coefficients are shown in Fig. 13(i–iii) respectively. Equation 20 is used as the loss function with weights l = 10 and n = 1. Clearly, the electron drift, trapping, detrapping and recombination coefficients follow the ground truth values. The learned recombination coefficients for the holes follow the ground truth values as well. For multiple trapping centers for holes (2 in this case), the learning-based model finds the equivalent trapping center, with equivalent trapping and detrapping lifetimes following Eqs. 18 and 19 respectively. The ground truth values of trapping 1 lifetime is 0.195 μ s and trapping 2 lifetime is 0.094 μ s corresponding to probability of trapping holes in trap center 1 and 2 to be 0.05 and 0.10 respectively. The ground truth equivalent trapping lifetime (τ eq ) is calculated using Eq. 18 to be 0.0634 μs. The fraction of holes getting trapped in

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the equivalent trapping center is 1 − 0.8541 = 0.1459. Similarly, in the ground truth simulation data, we considered fraction of charge getting detrapped from trap center 1 and 2 are 0.10 and 0.05 respectively. In the same manner, the detrapping 1 and 2 lifetimes are 94.9122 ns and 194.9573 ns respectively. Considering Eq. 19, and equivalent trapping probability as 0.1459, we compute the equivalent detrapping lifetime τ dt, eq as 145.9 ns. The fraction of holes remaining after detrapping from the equivalent trapping level would be 0.9338. Thus, the fraction of charges getting detrapped from the equivalent trapping center is 1 − 0.9338 = 0.0662. For the trained weights as shown in Fig. 13, the error values of drift coefficients (μe ), trapping (weT ), detrapping (weD ), recombination coefficients (weRec ) for electrons are 1.32 × 10−5 , 0.0412, 0.0316, 0.0277 respectively which are computed for voxels 9 to 99. Similarly, the error values of the equivalent trapping (whT, eq ), equivalent detrapping (whD, eq ), and recombination coefficients (wh, Rec ), for holes are 0.0954, 0.1957 and 0.3378 respectively which are computed for voxels 1–59. The arithmetic mean of the error of these material properties is 0.1042.

4.2.4

Numerical Experiments with Physical Model-4

The physical model-4 is trained with signals generated from motion due to electrons and holes separately. Figure 14 shows the hole trapping, detrapping and recombination coefficients due to electron-hole pair injection at voxel positions 24, 27 and 30 for different λ2 in Eq. 22. During training, the trapping hole and detrapping hole weights were bounded in [0.04, 0.07], and [0.15, 0.30] respectively which are close to the actual ground truth weights. The initialization of trapping, detrapping and recombination coefficients for holes are done uniformly at 0.05, 0.2, and 0.005 respectively. It is seen that for λ2 = 0, the hole trapping, detrapping and recombination coefficients does not converge to the ground truth hole coefficients. However, using T.V. regularization improves the convergence of these coefficients to actual ground truth values. For λ2 = 0.001 and 0.01, the hole trapping and detrapping coefficients are closer to the ground truth coefficients than for λ2 = 0.1 and hence smaller the error. However, for recombination coefficients, the trained weights for λ2 = 0.1, 0.01 and 0.001 are better than for λ2 = 0. Thus, it is seen that the weights λ2 = 0.01, 0.001 in the loss function of Eq. 22 provides better convergence for the hole coefficients. Additional simulation experiments have been done with λ2 = {0.001, 0.01} without bounds on trapping and detrapping coefficients and electron-hole pair injections at Voxels 24, 26 and 28. All the initial weights of trapping and detrapping over the voxels has been uniformly initialized as {0.005, 0.005}, {0.05, 0.2}, {0.07, 0.3} which corresponds to ‘far’, ‘ip1’ and ‘ip2’ respectively in Figs. 15 and 16. It is observed that bounds on the trapping and detrapping weights do not have any influence on the final trained weights of the holes. However, for λ2 = 0.001, the hole trapping, detrapping and recombination coefficients converge more closely to the ground truth parameters. Additionally, initializing the trapping and detrapping hole weights with ‘ip2’ provides better convergence to the trained weights.

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Fig. 14 Trapping, Detrapping and Recombination Hole Coefficients for hole injection at Voxels 24, 27 and 30 in Physical Model-4 with varying λ values as shown in the legend. Here λ refers to λ2 in Eq. 22. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [33])

Fig. 15 Trapping, Detrapping and Recombination Hole Coefficients for hole injection at Voxels 24, 26 and 28 in Physical Model-4 with λ = 0.001 as shown in the legend. Here λ refers to λ2 in Eq. 22. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [33])

Fig. 16 Trapping, Detrapping and Recombination Hole Coefficients for hole injection at Voxels 24, 26 and 28 in Physical Model-4 with λ = 0.01 as shown in the legend. Here λ refers to λ2 in Eq. 22. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [33])

Similar experiments have been done with varying λ1 = 0.1 in Eq. 22 with λ1 ∈ {0, 0.001, 0.01, 0.1}. The electron-hole pair injections are at Voxels 81, 84 and 87. It is seen that for λ1 = 0.1 in Eq. 22, the mean error value has the

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Fig. 17 (i) Drift, (ii) Trapping and Detrapping, and (iii) Recombination Electron Coefficients for electron injection at Voxels 81, 84 and 87 in Physical Model-4 with λ1 = 0.1 as shown in the legend. Here λ refers to λ1 in Eq. 22. Readers are suggested to enlarge the figure for closer view. (Figure adapted with permission [33])

minimum value of 0.0638. During training, the bounds on trapping, detrapping and recombination weights for electrons are bounded in [0.004, 0.012], [0.008, 0.02] and [0.0005, 0.005] respectively, while the initialization of trapping, detrapping and recombination coefficients for electrons are done uniformly at 0.012, 0.015 and 0.002 respectively. This is referred to as ‘bound’. Additional simulation experiments have been done with λ1 = 0.1 without bounds on trapping, detrapping and recombination coefficients with electron-hole pair injections at the same Voxels. The initialization of trapping, detrapping and recombination weights for electrons are done with the same values of {0.012, 0.015, 0.002}, {0.02, 0.02, 0.004} and {0.005, 0.009, 0.0005} which are referred as ‘same’, ‘grtr’ and ‘lt’ respectively. It is seen that for ‘grtr’ case, the mean error has the value of 0.1159 which is minimum of these three cases. Overall, the case with ‘bound’ provides us with the minimum error for the electron coefficients. Figure 17 shows the electron drift, trapping, detrapping and recombination coefficients for λ = 0.1 with ‘bound’ and ‘grtr’ cases. The material properties for the electrons converges very closely to the corresponding ground truth values.

4.3 Comparison of the Different Physical Models The performance of the different physical models is shown in Table 1. The mean relative error due to the electron coefficients (Err2(electrons)) are separated from that of holes (Err2(holes)) and the mean of Err2(electrons) and Err2(holes) are then computed as Err2(Total) in Table 1. For Physical Model-1, k = 1, l = 104 , n = 103 are used with electron-hole pair injections are voxel position 9 with stride of 5 voxels until voxel 59. For Physical Model-2, l = 10, n = 1 is used, with same electronhole pair injections as in Physical Model-1. For Physical Model-3, l = 10, n = 1, and the electron-hole pair injections are in the same voxel position as in Physical Model-1 and 2. In Physical Model-4, the electrons and holes coefficients are trained

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Table 1 Relative Error (in %) for the four different physical models Physical model 1 2 3 4 (holes only) 4 (electrons only)

Err2(electrons) 2.4104 2.6536 1.3443 × 5.1561

Err2(holes) 2.9942 3.6098 16.0488 3.2256 ×

Err2(Total) 2.7023 3.1317 8.6966 4.1909

separately. Hence, the Err2(electrons) only refers to the relative error result for the model trained for electron coefficients only. The electron injections are at voxel 81, 84 and 87 with λ1 = 0.1 with ‘bound’ condition as described in the previous subsection. The hole injections are at voxel 24, 26 and 28 with λ1 = 0.001 with ‘ip2’ condition as described in the previous subsection. It is seen that for Physical Models 1 and 2, the Err2(Total) value is small. On the other hand, for Physical Model 3, the Err2(holes) are maximum. This is because in the learned model, the hole coefficients (equivalent in this case) tend to oscillate around the ground truth value. Overall, the Err2(Total) is less than 9%, which shows good convergence of the RTSD material parameters to the ground truth values.

5 Discussion and Conclusion We demonstrate how machine learning can be used to characterize the Room Temperature Semiconductor Detector (RTSD) at a much finer scale spatially which is vital for developing more sophisticated algorithms and its implementation in large scale medical and industrial applications. We consider pixelated configuration of the RTSD detector in demonstrating our physics-based machine learning approach, but this method can be extended to other electrode configurations as well. The RTSD crystal is virtually discretized into small volumes or voxels where the physical laws governing the electron and hole charge motion in the RTSD holds true. A learning-based model has been developed by incorporating these physical laws – transport, trapping, detrapping and recombination of electron and hole charges for each of these voxels. The electron-hole charge pair is injected in this model at one or multiple positions and the outputs of the model are the signals at the electrodes, along with free and trapped charges in the crystal. The CZT detector in this model is considered to have 1 trapping center for electrons and 2 for holes. However, this physics-based machine learning approach can be extended to any number of trapping centers for electrons and holes. Once trained on the ground truth data, the learning model has the trained weights which are the material properties in terms of drift, trapping, detrapping and recombination coefficients for both electrons and holes.

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The data required to train the learning-based models must be generated in real world using several experimental setups and expertise. This is not repeatable and scalable for numerous RTSD crystals which are required for several applications. In order to address this issue, several reduced order models have been developed in Sect. 4 requires fewer data for training the model. One of our models, Physical Model-4 can identify most of the material properties just using the signals at the electrodes, which finds suitable application in current electronic sensor hardware setup. There are a few limitations of our physics-based machine learning approach in characterizing RTSDs. Our model has been developed by considering a forward physics model (classical model) as described in Sect. 2 of this chapter. However, there are other physical equations which describe the charge transport in RTSDs. Although our physics-based machine learning methodology for finding the material properties in micron scale is still valid for those forward models (classical models), the detailed implementation in that case needs to be carried out. Additionally, since this physics-based learning model has been based on equations used in a classical model, the physics-based learning model has the risks of “inverse crime” [58] when the same (or nearly the same) theoretical ingredients are employed to synthesize as well as invert data in an inverse problem. In order to avoid this pitfall, one way could be to use a relaxed theoretical model compared to the one exactly used as the forward model. Alternatively, a traditional machine learning or deep learning model can be used in conjunction with the physics-based learning model. In this work, the machine learning based models have been developed without considering noise such as Poisson noise, Quantization noise, Sampling Noise or other Statistical noise and actual experimental data from sensor hardware electronics. Developing models incorporating this information a priori is one of the future research directions. This physics-based machine learning also needs to be trained based on training data on GPUs. Although the training time is a few hours, but this also needs to be accounted for while implementing this model. However, this drawback exists in mostly all deep learning and artificial intelligence models, but since our physics-based model uses far less training weights, the training time is faster than conventional deep learning models and faster than the classical approaches using non-deep learning methods or experimental approaches. Overall, the chapter presents a novel approach of physics-based machine learning model for characterizing RTSDs. This work has been discussed in more details in [32–36, 57]. Our approach in characterization of the RTSD is the first novel approach in this field. Additionally, we have used most of the knowledge of the physical world in this model, some of which may vary from crystal to crystal. Development of learning-based models which use fewer physical laws, which can infer the physics from data is another interesting approach which is within the scope of future work. Incorporating the sensor models to image reconstruction and reuse of imperfect RTSD sensors is one the applications for the learning-based physical model. Our learning-based model can be extended to sub-pixel imaging and improve the quality of image reconstruction.

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High Energy Resolution X and Gamma Ray Imaging Spectroscopy with the ORION Multichip Readout Electronics Filippo Mele

1 Introduction The observation of the high energy transients coming from the deep space is a fundamental tool for the understanding of a multitude of astrophysical phenomena. Especially since 2017—when for the first time the simultaneous detection of gravitational waves (GWs) and short gamma ray bursts (GRBs) generated by the same binary neutron star merger has been observed [1]—a new era of multimessenger astrophysics started: observing the sky with a wide field of view and covering a large frequency range can be extremely useful to trigger the observation and accurate localization of GRBs, which, in turn, enable the search of GWs associated with these intense and wide-range electromagnetic emissions, from the radio spectrum up to gamma-rays [2]. Due to the absorption of X and .γ photons in the atmosphere, balloon-borne [3] and satellite instrumentation are required for such specific purpose. With the aim of realizing a comprehensive census of GRBs, with special focus on high red-shift GRBs, the THESEUS (Transient High Energy Sky and Early Universe Surveyor) space mission concept has been proposed for medium-class ESA (European Space Agency) calls [4]. Providing a substantial advancement in time-domain astronomy through detection, accurate location, multiwavelength (0.3 keV to 10 MeV) characterization, and red-shift measurement, of many classes of high-energy transients, THESEUS will have a unique capability to serve the scientific community in this sense, providing a powerful synergy with the ground observation stations and next generation large facilities for GWs and neutrino detectors [5]. The scientific payload of the THESEUS satellite will exploit the combination of three on-board instruments, covering the energy bands from the

F. Mele () Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_5

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near infrared up to gamma rays with an unprecedented monitoring capability on the GWs electromagnetic counterparts: • Infra-Red Telescope (IRT) [6]—the IRT is a 70 cm diameter class near-infrared telescope with .∼15 arcmin field of view in the 0.7.−1.8 .μm wavelength range. The IRT is designed to localize and study the GRB afterglows [7] detected either by the SXI or the XGIS instruments. The IRT can work both in imaging and in low-resolution spectroscopy mode. • Soft X-ray Imager (SXI) [8]—the SXI is a set of two “Lobster-Eye” X-ray telescope [9], for a total field of view of 0.5 steradiant with a ITH (see Fig. 6b), the circuit behaves in the opposite way. The current difference Idisc switches Mdown on, while Mup is off. The input impedance Zin and the switching time are considerably reduced

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by a negative loop gain provided by the second part of the TIA. The loop gain can be calculated with the following expression: Gloop = −(gmA + gmB )(roA ||roB ),

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where gm,up|down is alternatively the transconductance of the transistor Mup|down , depending on discriminator operation. When the current discriminator is fired, its output features a time-over-threshold (ToT) value depending on the input charge levels. In particular, for higher input charges, the ToT will be longer than for lower input charges. Thus, the rising and falling edges of the output pulse will come earlier and later, respectively, than for a lower input charge. The rising and falling edges arrival times are of fundamental importance for the functioning of the charge sharing correction logic. A baseline holder has been designed to reduce variations coming from transistor mismatches of the threshold current with respect to the input current. The DC feedback block copies the current Isum , filters it leaving the DC component, and gives it back to the threshold branch. In the ideal case, the threshold current is precisely equal to the DC component of the signal current. Thus, no more dependency exists on mismatches coming from previous stages, and only mismatches in the DC feedback block affect the threshold current. Hence, a DAC current IDAC sets the threshold of the desired value above the noise limit and recovers the mismatches. Reducing variations allows for designing a DAC with a lower number of bits, lower FSR, and finer LSB, thus saving area. Table 3 reports the main parameters of the MIRA current discriminator in SP mode and with an input charge Qin = 1000 e- . Table 3 The MIRA current discriminator main parameters in SP mode with an input charge Qin = 1000 e-

Parameter Isum,peak [.μA] .σn,isum [nArms ] .σn,Qsum [e rms ] ENC [e-rms ] .τLPF [ns] .σIth−Isum,DC [nArms ] DAC LSB [nA]

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2.4 The Charge Sharing Correction Logic In a photon counting application employing a microchannel plate (MCP) as a detector, the charge sharing effect may happen when the total charge exiting the MCP is not captured by a single pixel. In this case, it would be shared by many nearby ones due to electron cloud diffusion. Indeed, mistakes like missing part of the events and counting excess events in more than one pixel might lead to a reduction in detection efficiency. Thus, the goal of the charge sharing correction logic is to avoid multiple counts and degradation of the spatial resolution. It is performed by comparing the outputs of current comparators of different pixels and assigning the count to the pixel that collected the highest charge. In this way, a spatial resolution limited to the 35 .μm pixel size may be achieved even in the case of charge sharing. MIRA features three different modalities. Moreover, depending on modality choice, the MIRA filter stage can be configured either in Single Pixel (SP) mode or Charge Summing (CS) mode. The three modalities are Mode1, Mode2, and Mode3. In Mode1, the MIRA filter stage works in single pixel (SP) mode, and the charge sharing correction logic is excluded. Indeed, each pixel works independently and with its own collected charge. Then, the current comparator output pulse is fed to the pixel counters, incrementing the stored value. In Mode2, the filter stage is configured in single pixel mode, and the Mode2 charge sharing correction logic is enabled. Thus, in the case of charge sharing, the charge exiting the MCP is collected by each pixel in different amounts depending on the position of the electron cloud. Then, it is processed by the CSA and amplified by a factor of four by the filter stage. Once the signal has reached the current comparator, it will be compared with the threshold, and an output pulse will be generated. The path is the same as in Mode1. Since the Mode2 algorithm has been enabled, comparisons between the other pixel pulses are performed to find the pixel with the highest collected charge. The comparisons are both in the vertical and the horizontal directions. Hence, the winning pixel would be the one with four arrows pointing to it. In each pixel, the process of finding the pixel with the highest amount of charge is based on a comparison performed by the MUTEXes arbitrators. When the discriminator fires, it generates a pulse with a temporal width according to the amount of charge accumulated by the pixel. Following that, the pulse is transferred to the MUTEXes. They are responsible for choosing between two requests and activating an acknowledgment signal for only one request, even when many requests come simultaneously. The operation principle of the MUTEX is, thus, based on the decision of which pulse arrives first and lasts more. They are based on an RS latch with a simple structure (U3 and U4) to eliminate glitches at the output and to filter the metastable state occurring when two inputs arrive closely spaced in time. Figure 7 shows the Mode2 schematic based on the MUTEX comparisons of a cluster of four pixels, i.e., pixel F, G, L, and M. Pixel M has collected the highest amount of charge (1400 e- ), thus its counter is fired. The Mode3 charge sharing correction logic is, in principle, an extension of Mode2. Moreover, the filter stage is configured in charge summing mode (CS). In

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CS mode, each pixel summing node receives the charge from adjacent pixels on the top, top-left, and left sides of the considered pixel. Indeed, unlike in Mode2, the total initial charge may be reconstructed in the case of charge sharing. As for Mode2, the logic operates for a cluster of four pixels. The summing node that reconstructs the total charge is located in the center of the four pixels cluster and, for this reason, is called the central summing node. Thus, in the case of charge sharing, a twostep algorithm finds the winning pixel, starting from comparisons between summing nodes. Firstly, it identifies the four pixels cluster where the charge is present, i.e., where the central summing node is located. Then, it finds the pixel in the cluster that collected the highest amount of charge by making comparisons with summing nodes around the selected cluster. Imaging simulations considering the charge dispersion of the MCP charge cloud and modeling the pixel electronic noise and the pixel threshold dispersion validate the implemented algorithms. The simulation model of the charge cloud follows the 2D Gaussian probability density function distribution with standard deviations in the x and y directions of .σx = 7 .μm and .σy = 9 .μm. Moreover, the pixel fill factor FF = 33% has been taken into account. A beam of electrons, with QMCP = 4000 e- , has been scanned with a step of 500 nm in both x and y directions, over a matrix of 6.×6 pixels, for 1000 times. Figure 8 shows the simulation results for the Mode1 and Mode2 algorithms. The resulting image is a composition of an array of 3.×3 images, where each image corresponds to a specific pixel and shows the number of counts at each step of the beam scanning. The number above each image represents

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the threshold level of that pixel after the DAC correction. Ideally, each pixel should count the events only when the beam is scanned inside its area, while it should never count when the beam is elsewhere. Thus, the result should be a uniform white area image at the location of the considered pixel. Figure 8a shows the simulation results without the charge sharing correction logic (Mode1). It can be noticed that each pixel counts even when the charge cloud is centered in the area of others, thus causing a worsening of the spatial resolution. Figure 8b shows the simulation results with the Mode2 algorithm enabled. The algorithm of Mode2 compares the discriminator output of pixels on the top, left, right, and bottom sides of the considered pixel. This should allow only one pixel to count for each event in whatever position it originated. Indeed, each pixel detects the event only when the latter is inside the pixel area, granting thus a spatial resolution limited to the pixel size (35 .μm).

2.5 MIRA Readout Stage The output of the charge sharing correction logic is fed to the pixel readout stage. The readout stage of the pixel is composed mainly of two 17-bit counters that will increment their value each time a hit is assigned to the pixel. The two counters work alternatively to have a zero-dead time operation, meaning that, while one counts the events, the other is read by the chip periphery. In this way, a continuous counting and reading phase is guaranteed. During the counting phase, one counter receives the events from the charge sharing correction logic and increments the stored number. During the counting phase, the same counter behaves like a Shift Register (SR), moving its content to the bottom pixels (with one of the two counters configured as an SR) until it reaches the End-Of-Column block (EOC), i.e., the chip periphery. The two pixel counters have been implemented as 17-bit Linear Feedback Shift Register (LFSR) that are able to work in the two modalities and, thus, saving occupation area [9]. Figure 9 shows the implementation of the two 17-bit LFSRs (for clarity, only three FFs out of seventeen are represented in the figure). Moreover, inside each pixel, a 7-bit Pixel Configuration Register (PCR) is also present. It is composed of seven FFs that store the pixel configuration bits. They consist of the four DAC bits used for the pixel threshold programming, one sign bit used for reducing the threshold current, one “CSA Mask” bit for decoupling the CSA from the rest of the circuit in case of malfunctioning, and one bit used to activate the injection network, i.e., a network responsible of testing the pixel electronics by an external signal. The PCR is attached to the last seven FFs (from Q11 to Q17 ) of only one counter. Figure 9 also shows the implementation of the PCR for just one pixel. To reduce the complexity of the figure, only two FFs of the PCR are represented.

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3 Experimental Results The MIRA ASIC has been characterized both in a laboratory setup and in the photon-counting unit (see Sect. 1) without the microchannel plate, showing similar results. This section describes the characterization of the MIRA CSA and the charge sharing correction logic. In each pixel, an injection capacitance Cinj is present to pulse each pixel. Hence, an equivalent input charge may be injected into each MIRA CSA by an input square wave. The relationship between the amplitude Vtest of input test signal and the CSA output amplitude Vout,amp is: Vout,amp = Vtest

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An amplitude of the CSA output voltage Vout,amp = 112 mV, a rising time trise = 7 ns, and a falling time tfall = 150 ns, thus a shaping time .τs = 261 ns, have been achieved. The measured shaping time and the output voltage amplitude are close to the simulated values. Since the measurement setup add a not negligible contribution to the signal rise time, the measured rise time is slightly lower than the expected one of 2 ns (a rise time faster than 7 ns is expected in a real operation). Moreover, since the rms noise introduced by the active probe is higher than the rms noise expected

MIRA: A Low-Noise Pixelated ASIC for Photon Counting Applications Fig. 11 MIRA charge sharing correction logic characterization, Mode1 and Mode2. The pixels cluster is highlighted with a red box. The equivalent charge cloud has been rotated inside the cluster by changing the input charge from time to time. In every case, all pixels count in Mode1. In Mode2, only the pixel with the highest charge amount is counting. The spatial resolution is limited to the pixel size

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at the CSA output, an SMA connection has been employed to better quantify the noise performances of the stage. In Fig. 10b, the measured CSA transient response shows an rms output voltage noise .σn,vout = 750 .μVrms that corresponds to an ENCCSA = 27 e-rms at the CSA level. Hence, an ENC = 20 e-rms is achieved thanks to further filtering by the Filter Stage. It can be concluded that measurements of the MIRA CSA showed transient characteristics and noise performances in line with simulations. The MIRA charge sharing correction logic (CSCL) has been tested by replicating a real operating environment. Indeed, since MIRA has been characterized without the microchannel plate, different charge levels are provided to the pixels of one cluster. When the chip is configured in Mode1 modality, the MIRA CSCL is excluded. Thus, all four pixels discriminate the event and will count it. The spatial resolution is degraded and limited to the cluster dimensions. The Mode2 modality should be selected to avoid multiple counting inside the cluster and to assign the count to the pixel with the highest amount of collected charge. Figure 11 shows the results in Mode1 and Mode2. The four pixels cluster is highlighted with a red box. The equivalent charge cloud has been rotated inside the cluster by changing the pixels injected charge from time to time. In every case, all pixels count in Mode1. In Mode2, only the pixel with the highest charge amount counts. Thus, the spatial resolution is limited to the pixel size (35 .μm). Mode3 has been tested in a similar way, showing analogous results to Mode2 in terms of spatial resolution. In this test, the charge resolution for which the charge sharing correction logic can correctly

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distinguish the pixel with the highest charge from the others is 150 e- , limited by the test setup. It is expected to be lower during real operation (with the MCP and the charge sharing effect), determined only by the pixel mismatches inside the cluster.

4 Conclusions We have introduced the design of a charge readout ASIC. The key features achieved by this design are the compactness of the pixels (of only 35 .μm side with an anode fill factor of 32.%) and the very low noise. The main challenge of densely pixelated detectors is charge sharing among neighboring pixels: consequently, we have endowed the chip with different types of charge correction logic. Another key challenge is the layout of the ASIC, in particular of the bonding pads that should be grouped on a single side in order for the several chips to be tiled (on three sides) to cover larger detector areas. The growth in the number of pixels also impacts the time for data readout along the serial bus. We expect that the number of pixels can grow by a factor between 100 to 1000 and still be compatible with the zero dead-time condition and a feasible frequency of the digital clock that has to be correspondingly increased. In addition to MCPs, this ASIC could be coupled to other types of detectors, in particular semiconductor ones, for multispectral X-ray and gamma-ray imaging applications.

References 1. Arridge, C. S., et al. (2012). Uranus Pathfinder: Exploring the origins and evolution of Ice Giant planets. Experimental Astronomy, 33(2), 753–791. 2. Hofstadter, M., et al. (2017) Ice giants pre-decadal survey mission study report. JPL D-100520. 3. Ghail, R. C., et al. (2012). EnVision: Taking the pulse of our twin planet. Experimental Astronomy, 33(2), 337–363. 4. Pelizzo, M. G., et al. (2021). The PLanetary extreme Ultraviolet Spectrometer Project. In Astronomical optics: Design, manufacture, and test of space and ground systems III (vol. 11820). Bellingham: SPIE. 5. Fabbrica, E., et al. (2022). Design of MIRA, a low-noise pixelated ASIC for the readout of micro-channel plates. Journal of Instrumentation, 17(1), C01047. 6. Fiorini, C., & Porro, M. (2004). Integrated RC cell for time-invariant shaping amplifiers. IEEE Transactions on Nuclear Science, 51(5), 1953–1960. https://doi.org/10.1109/TNS.2004.835578 7. Krummenacher, F. (1991). Pixel detectors with local intelligence: An IC designer point of view. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 305(3), 527–532. https://doi.org/10.1016/ 0168-9002(91)90152-G 8. Ballabriga, R., et al. (2007). The Medipix3 prototype, a pixel readout chip working in single photon counting mode with improved spectrometric performance. IEEE Transactions on Nuclear Science, 54(5), 1824–1829. 9. Cusick, T. W., & Stanica, P. (2017) Cryptographic Boolean functions and applications. Cambridge: Academic Press.

Development of the Analog Front-End Circuit for the CMS Pixel Readout Chip at the HL-LHC L. Gaioni, A. Galliani, M. Manghisoni, L. Ratti, V. Re, E. Riceputi, and G. Traversi

1 Introduction Phase-II upgrades of CMS and ATLAS at the High-Luminosity (HL) Large Hadron Collider (LHC) require new trackers to deal with extraordinary particle rates and radiation levels [1, 2]. Advanced pixel sensors, in the crowded region surrounding the interaction point, will handle rates close to 3 GHz/cm.2 , with a total ionizing dose (TID) expected to be about 1 Grad(SiO.2 ), with a 1 MeV neutron equivalent fluence of 2.×10.16 n.eq cm.−2 accumulated over around 10 years of operation. In the innermost layers of the tracker, an elementary pixel size of 50 . × 50 .μm (or, alternatively, 25 .× 100 .μm) will improve momentum measurement accuracy. While sensors with a typical thickness close to 300 .μm are currently in use in the experiments, thinner sensors, with an active volume around 100 .μm, will be used in the phase-II upgrades [3, 4]. On one hand, sensor radiation hardness will naturally benefit from a reduced device thickness, but, on the other hand, the amount of charge and, thus, the signal delivered by the pixels will be smaller. The readout chips will be required to be fully functional at low thresholds (1000 electrons or lower) in order to preserve the detection efficiency of the system. This will tighten up the requirements on both the noise and threshold dispersion performance of the analog front-end, where the per-pixel power consumption has to be limited (to about 6 .μW) to meet the specifications set by cooling and power-delivery systems.

L. Gaioni () · A. Galliani · M. Manghisoni · V. Re · E. Riceputi · G. Traversi Università di Bergamo, Dalmine, Italy INFN, Sezione di Pavia, Pavia, Italy e-mail: [email protected] L. Ratti Università di Pavia, Pavia, Italy INFN, Sezione di Pavia, Pavia, Italy © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_7

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The RD53 collaboration [5] was established at CERN in 2013 to tackle, in a commercial 65 nm CMOS technology, the design of high performance readout chips for the high-luminosity upgrades of the CMS and ATLAS experiments. The collaborative effort of the two communities led to the submission, in 2017, of the first large-scale demonstrator chip, called RD53A [6]. RD53A includes a matrix of 400 .× 192 readout channels, featuring a cell size of 50 . × 50 .μm, that can be bonded to the sensor through dedicated bump pads laid out in the topmost metal layer. Three different analog front-end architectures, called Synchronous, Linear and Differential, were specifically developed and integrated in the RD53A chip, whose pixel matrix is split in three regions each hosting one front-end flavor. In particular, 128 columns were allocated to the Synchronous front-end, whereas 136 columns were assigned to both the Linear and the Differential front-ends. The three analog processors have been thoroughly investigated in view of their integration into the production chips [7], with the Linear front-end being chosen for the final integration in the CMS chip, and the Differential for the ATLAS one. After RD53A characterization, a number of bug fixes and design improvements were proposed and implemented in the second generation of RD53 readout chips, referred to as RD53B. In particular, some modifications to the RD53A Linear frontend were needed to improve the time-walk performance of the readout channel and its threshold tuning capabilities in specific operating conditions [8]. In this work, the RD53B Linear front-end circuit will be described, discussing the main modifications with respect to the RD53A version and the results relevant to the testing of a small prototype chip including both the RD53A and RD53B frontend flavors. In particular, the overall architecture of the analog processor will be introduced in Sect. 2 along with a discussion of the optimization process which led to the RD53B design. Section 3 is concerned with the key test results, as obtained from the characterization of the prototype chip before and after irradiation up to a total ionizing dose of 1 Grad(SiO.2 ).

2 Front-End Design The Linear front-end architecture is shown, with some transistor level details, in Fig. 1. Such an architecture implements a shaper-less readout chain including a charge sensitive amplifier (hereafter referred to as CSA or preamplifier) and a comparator, exploited, together with a Time-over-Threshold (ToT) counter (not shown in the figure), for analog to digital conversion of the input signal amplitude. The front-end circuit also includes a threshold tuning DAC (TDAC), acting on the output of the first stage of the comparator, needed to reduce the threshold dispersion of the front-end and making operations with a threshold level close to 1000 electrons possible. An injection circuit, emulating the signal delivered by the sensor, is connected to the preamplifier input, while an actual sensor can be connected to the front-end through a dedicated, octagonal pad about 16 .μm wide. A description of the blocks integrated in the Linear front-end is given in the following sections.

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VDDA

CK Injection circuit

IK/2

M3 CF Vo,csa Transconductance

detector bump PAD

Vo,comp Tr ff

stage

V

M2

M1

Vth Vref

TDAC code Itrim

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Fig. 1 Block diagram of the Linear front-end

2.1 Charge Sensitive Amplifier The preamplifier integrates a folded cascode gain stage surrounded by a Krummenacher feedback network [9] featuring a differential pair biased with a current .IK . The Krummenacher feedback serves a two-fold purpose: on one hand it guarantees proper operation of the front-end also in the presence of leaky detectors, and on the other hand it provides a linear discharge of the CSA feedback capacitance, .CF . In steady state, half of the .IK current is sourced by transistor .M2 (whose drain is connected to a current generator .IK /2) while the remaining half flows through .M1 . Since the current in the matched pair .M1 and .M2 is the same, the preamplifier DC output voltage is locked to .Vref . In the presence of a detector leakage current the output of the preamplifier tends to increase, rising the current in .M2 and, thus, charging the capacitor .CK . As a result, the gate of .M3 is driven low, and the transistor carries the additional current which compensates for the detector leakage one. On the other hand, for fast signals the leakage compensating loop (which reacts to extremely low frequency signals) does not kick in, the output voltage increases and the drain current of .M1 is reduced. Nonetheless, the current in .M3 does not change, and part of this current (or the entire current in case of saturation of the differential pair .M1 -.M2 ) discharges the feedback capacitance .CF , thus restoring the CSA baseline. When saturation of the differential pair takes place (this happens for an input charge larger than around 2000 electrons in the actual implementation of the front-end), the Krummenacher feedback thus provides a linear discharge of .CF . With a current of 3 .μA flowing in the input branch of the folded cascode gain stage, the preamplifier is the main contributor to the total power consumption of the Linear front-end. By using a single pole approximation for the CSA forward gain stage, the preamplifier transfer function, .F (s), can be written as:

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F (s) =

.

s(1 + sτ3 ) Vo,csa 2CK  , Qin gmn gmp (1 + sτ1 )(1 + sτ2 )(1 + sτ3 )(1 + sτ4 )

(1)

with .Vo,csa being the Laplace transform of the preamplifier output signal, .Qin the input charge, .gmn and .gmp the transconductance of .M1 (or .M2 ) and .M3 , respectively. It can be shown that τ1 

CK ,. gmp

(2)

τ2 

CF ,. gmn /2

(3)

τ3 

CA ,. 2gmn

(4)

τ4 

CD τp , CF A0

(5)

.

where .CA is the parasitic capacitance at the source of .M1 and .M2 , .A0 the DC gain of the CSA forward stage and .τp the time constant associated with its dominant pole. In simulations, such values were found to be 76 dB and 140 kHz, respectively. In (5), .CD models the sensor and the parasitics capacitance shunting the preamplifier input. To avoid instabilities in the front-end operation, it has to be ensured that .τ1 . .τ2 . .τ3 . .τ4 . The transfer function in (1) can be simplified by assuming .CK → ∞ and .CA → 0. Under this hypothesis, it is possible to write F (s) 

.

2/gmn . (1 + sτ2 )(1 + sτ4 )

(6)

In the time domain, the response of the preamplifier to a Dirac delta-like current pulse, .δ(t)Qin , is given by vo,csa (t)  U (t)Qin

.

− τt

2 e gmn

− τt

−e τ2 − τ4 2

4

,

(7)

U (t) being the unit step function. Assuming .τ2  τ4 , the response of the CSA can be written as

.

vo,csa (t)  U (t)

.

 Qin  −t/τ2 e − e−t/τ4 . CF

(8)

The peaking time, .tp , at which the CSA output voltage gets to its maximum can be shown to be

Development of the Analog Front-End Circuit for the CMS Pixel Readout Chip. . .



τ2 .tp  τ4 ln τ4

133

 (9)

,

which is an increasing function of .τ2 . This means that the larger the Krummenacher current .IK , the larger the transconductance of .M1 and .M2 and, in turn, the smaller the peaking time. The charge sensitivity of the CSA (i.e. the charge to voltage gain of the preamplifier) can be computed as the peak value of the Laplace anti-transform of .F (s). For very small values of .gmn , and this is the case of the front-end discussed in this work, where the Krummenacher current is typically set around 25 nA, the charge sensitivity, .GQ , can simply be written as GQ 

.

1 . CF

(10)

Both the RD53A and RD53B front-end flavours have been designed with a target charge sensitivity close to 150 mV/fC. For input signals larger than around 2000 electrons, the response of the preamplifier cannot be modelled by (8), since the differential pair .M1 -.M2 , as already mentioned, gets saturated. In this condition, .M1 is turned off and the current .IK /2, flowing in .M3 , linearly discharges the CSA feedback capacitance. The preamplifier response to a large input signal can thus be modelled by means of vo,csa (t) =

.

 IK Qin  1 − e−t/τ4 − t. 2CF CF

(11)

The discharge process is completed for .t > t0 , where the output voltage returns to its baseline value. .t0 is such that .

 Qin  IK 1 − e−t0 /τ4 − t0 = 0. CF 2CF

(12)

The response to a large signal can thus be approximated by means of a triangular pulse with a peak value occurring at the time .tp∗ given by ∗ .tp



2Qin = τ4 ln IK τ4

 ,

(13)

which is a monotonically increasing function of the input charge .Qin .

2.2 Noise Performance In order to operate the front-end with a threshold close to 1000 electrons and a noise occupancy not exceeding 10.−6 , as requested by the RD53A and RD53B

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specification documents, noise optimization is of paramount importance. The main contributions to the Linear front-end noise come from the CSA input device and from the transistors in the Krummenacher feedback network. The mean square noise at the preamplifier output, .vn2 , can be computed as vn2 = vn2in + vn2p + vn2d ,

(14)

.

where .vn2in is the contribution given by the CSA input device, .vn2p is the one relevant to the PMOS transistor .M3 , and where .vn2d takes into account the noise sources associated with the differential pair .M1 -.M2 . The noise contribution of the preamplifier input transistor is mainly due to channel thermal noise. By neglecting the flicker noise contribution, .vn2in can be written as vn2in =

.

2kB T γin (CD + CF )2 πgmin



∞

ω2 |F (j ω)|2 dω,

(15)

0

where .kB is the Boltzmann’s constant, T is the absolute temperature, .gmin the transconductance of the CSA input device and .γin its channel thermal noise coefficient, depending on the degree of inversion of the device channel [10]. By computing the integral in (15), and assuming .τ2  τ4 , it is possible to write vn2in 

.

4kB T γin (CD + CF )2 kB T γin (CD + CF )2 A0 = 2 gmin CF CD τp gmin gm τ22 τ4 n

(16)

which shows the dependence of .vn2in on the total capacitance, .CD , shunting the preamplifier input and on the gain bandwidth product of the CSA forward gain stage. Similarly, the noise contribution associated with .M3 and the one relevant to the differential pair are given, respectively, by vn2p 

.

2 .vn d

2kB T γp gmp



π

2kB T γn gmn  π

∞

|F (j ω)|2 dω =

0



2    F (j ω) dω = kB T γn ,  2 CF

∞ 1 0

2kB T γp gmp CF gmn

(17)

(18)

where .γn and .γp are the noise coefficients of transistors .M1 (or .M2 ) and .M3 , respectively. Equations 17 and 18 have been obtained, again, by neglecting the 1/f noise contribution of the transistors. The noise properties of a charge preamplifier are generally expressed in terms of equivalent noise charge (ENC), which is defined as

Development of the Analog Front-End Circuit for the CMS Pixel Readout Chip. . .

ENC 2 =

.

vn2 . G2Q

135

(19)

By combining (10) with (14)–(18), it is possible to write  ENC 2  kB T CF

.

gmp (CD + CF )2 γin A0 +2 γp + γn . CD gmin τp gmn

(20)

It is worth noticing that, in (20), the ENC depends on the .A0 /(τp gmin ) ratio, which is a constant function of .gmin . This means that changing the current biasing the preamplifier input device and, thus, its transconductance, should not, in theory, have an impact on the noise properties of the analog processor. Also, when the front-end is coupled to a non-leaky detector, the ratio .gmp /gmn is close to 1, since transistors .M1 and .M3 , operated in weak inversion, carry the same current .IK /2. On the other hand, the transconductance of .M3 is larger than the one of .M1 in the presence of leakage, leading to a non negligible rise in the ENC.

2.3 Threshold Discriminator The schematic diagrams of the threshold discriminators integrated in the RD53A and RD53B Linear front-ends are shown in Figs. 2 and 3, respectively. The first stage of the comparator is implemented by means of a transconductance stage, which outputs a current, .IGm , whose polarity depends on the difference between .Vo,csa , the output of the preamplifier, and the global threshold voltage, .Vth . Such a current signal represents the input of the subsequent stage, featuring a Träff transimpedenace amplifier (TIA) [11]. As shown in Fig. 1, the .Vo,c signal is sent to a couple of inverters, which consolidate the logic levels that will be fed to the digital circuits for ToT conversion of the input charge signal. Fine tuning of the threshold is accomplished by properly setting the TDAC code controlling the .Itrim current, drained from the output of the transconductance stage. The actual implementation of the tuning DACs integrated in the RD53A and RD53B versions of the front-end will be discussed in the next subsection. The transfer function, .TC (s), of the comparator can be computed as: TC (s) =

.

Rf Vo,c  Gm , Vo,csa 1 + sτc,cl

(21)

Rf Ci + gm4 )(ro3  ro4 )

(22)

where τc,cl 

.

(gm3

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M2a

Ci

Vo,csa

M4

iin,tia M2b

IGm

+

v

Gm M3 M1b

Vth M1a

TDAC Itrim

Fig. 2 Schematic diagram of the threshold discriminator integrated in the RD53A Linear frontend

Vdd

Ci

Vo,csa IGm

+

M2

M4

iin,tia

v

Gm M3

Vth

M1 M5

TDAC

Cm

Vbias

Itrim

Fig. 3 Schematic diagram of the threshold discriminator integrated in the RD53B Linear front-end

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is the closed-loop time constant associated with the input node of the Träff transimpedenace amplifier. In the previous equations, .Gm is the trasconductance of the input stage, .gmi and .roi are the transconductance and the output resistance of transistor .Mi , whereas .Ci and .Rf represent, respectively, the input capacitance and the equivalent feedback resistor of the TIA. It can be easily shown that the open-loop time constant, .τc,ol , associated with the TIA input is τc,ol = Rf Ci .

.

(23)

Hence, the closed-loop time constant is significantly faster than the open-loop one, provided that .(gm3 + gm4 )(ro3  ro4 ) is large enough, and the negative feedback of the TIA improves the timing performance of the comparator. The main difference between the comparator integrated in the RD53A and RD53B Linear front-end is the lack of diode-connected transistors .M1b and .M2b in the RD53B flavour. This has an impact on the equivalent feedback resistance, .Rf , of the transimpedance amplifier. In particular, for the RD53A design, such a resistance is given by: Rf =

.

⎧ ⎨

1 gm1a ⎩ 1 gm2a

+ +

1 gm1b 1 gm2b

, iin,tia < 0 , iin,tia > 0,

(24)

where .iin,tia is the input current of the TIA stage, whereas for the RD53B version Rf =

.

⎧ ⎨

1 gm1 , ⎩ 1 , gm2

iin,tia < 0 iin,tia > 0.

(25)

By assuming the same transconductance of the transistors integrated in the feedback path of the TIA, it is possible to conclude that the equivalent feedback resistor for the RD53B version is a factor of 2 smaller than the one obtained in RD53A. This, in turn, means that the time constant .τc,cl is, ideally, a factor of 2 smaller in the RD53B design. Moreover, the lack of .M1b and .M2b in the RD53B flavour, which were added in RD53A to minimize the current consumption of the TIA gain stage (implemented by means of .M3 and .M4 ), extends the current range of .iin,tia for which the stage operates in the linear region, boosting the response speed of the comparator. In order to keep the power consumption of the transimpedance amplifier under control, a starving transistor, .M5 , has been added in the RD53B front-end. As shown in the test results discussed in the next section, the improved RD53B design has a profound impact on the time-walk performance of the front-end. In particular, a time-walk smaller than 25 ns (i.e. the LHC bunch crossing period) can be achieved with the RD53B analog processor. This, in turn, makes it possible to operate the front-end with low in-time thresholds, as requested by RD53 specifications [12], which set a minimum in-time threshold of 1200 electrons (meaning that 50% of 1200 e.− hits are in time).

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VDDA IK/2

Vth4

M4

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M8

M9 to TIA

Vo,csa

VthFE

Vth6,7 M7

M6 Vth1,2

Vth

M2

M1

IB Vref IK

M5 Vth5

Fig. 4 Schematic digram for the threshold dispersion analysis. The device threshold voltage mismatch is modelled by mens of the voltage sources .Vthi,j and .Vthk

2.4 Threshold Dispersion Analysis Very low threshold dispersion is a must in order to operate the front-end at thresholds close to 1000 electrons. As discussed in the next subsection, the threshold dispersion is optimized in the Linear front-end by means of an in-pixel, currentmode tuning DAC. Nonetheless, having a small un-tuned threshold dispersion is, in general, strongly desirable, since lower TDAC resolution and power consumption are required. In this section the un-tuned threshold dispersion analysis is carried out with the aid of Fig. 4, which shows the devices, in the Krummenacher feedback network and in the transconductance stage of the comparator, mostly contributing to the threshold dispersion. In this analysis, only the threshold voltage mismatch between nominally identical transistors will be taken into account in order to evaluate the front-end threshold dispersion. In Fig. 4, the mismatch in the devices is modelled by means of the following voltage sources: • .Vth1,2 , which models the mismatch in the differential pair .M1 and .M2 integrated in the Krummenacher feedback; • .Vth4 , which accounts for the threshold variations in the transistor, .M4 , generating the .IK /2 in the Krummenacher feedback; • .Vth5 , modeling the mismatch in .M5 , which acts as the tail current generator .IK for the differential pair .M1 and .M2 ; • .Vth6,7 , which models the mismatch for the input transistors of the comparator;

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• .Vth8,9 , modeling the mismatch in the current mirror load of the comparator input stage. According to the well-know model described in [13], it is possible to write the variances σ 2 (Vthi,j ) =

.

σ 2 (Vthk ) =

.

A2Vth Wi,j Li,j

(26)

,

2 1 AVth , 2 Wk Lk

(27)

where .Vthi,j is the threshold difference between matched transistors .Mi and .Mj (.M1 -.M2 , .M6 -.M7 and .M8 -.M9 ) and .Vthk is the difference between the actual threshold voltage for an individual device .Mk (.M4 and .M5 ) and its nominal threshold. .AVth is a process dependent parameter, commonly provided by the foundry. The front-end threshold dispersion, referred to the comparator input, can be modelled by means of a voltage source .VthF E , whose standard deviation is given by σ (VthF E ) =

.

σ 2 (VthCSA ) + σ 2 (VthCOMP ),

(28)

with .σ (VthCSA ) being the threshold dispersion contributed by the charge sensitive amplifier, and .σ (VthCOMP ) the one associated with the comparator. The first term in (28) can be shown to be σ 2 (VthCSA ) =σ 2 (Vth1,2 ) + 4 .

+4

2 gm 4 2 gm 2

2 gm 5

σ 2 (Vth5 )

2 gm 2

(29)

2

σ (Vth4 ),

whereas the second one can be written, assuming linear operation for the comparator, as σ 2 (VthCOMP ) = σ 2 (Vth6,7 ) +

.

2 gm 8 2 gm 6

σ 2 (Vth8,9 ),

(30)

with .gmi being the transconductance of the transistor .Mi . The front-end inputreferred threshold dispersion, .σ (Qth ), can thus be computed by dividing (28) by the charge sensitivity of the preamplifier:

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σ (Qth ) =

.

σ (VthF E ) . GQ

(31)

According to (26) and (27), a way to reduce the un-tuned threshold dispersion is to increase the gate area of the transistors. This should actually be done carefully, since increasing the size of the Krummenacher feedback devices, may lead to instabilities in the preamplifier. In particular, by increasing the size of .M1 , .M2 and .M5 , the capacitance .CA (described in section II.A) gets larger, pushing the time constant .τ3 towards .τ2 and, in the end, degrading the phase margin of the preamplifier. Moreover, larger comparator transistors, may affect the value of the capacitance .Ci shunting the transimpedance amplifier input, slowing down the response speed of the comparator. Hence, a compromise between threshold dispersion, speed and stability has to be found.

2.5 Threshold Tuning DAC The fine-tuning of the threshold is addressed by means of a current-mode DAC generating a current, .Itrim , at the output of the transconductance stage of the comparator, as shown in Figs. 2 and 3. Figures 5 and 6 show the schematic of the TDACs integrated in the two front-ends. Both the analog processors implement a binary weighted DAC architecture with a resolution of 4 bits for RD53A and 5 bits for RD53B. While cascoded current mirrors were used in the RD53A version of the TDAC, a more compact design has been laid out in the RD53B front-end, featuring regular current mirrors. The DAC switches (.Mb ) are implemented by means of NMOS devices for both the front-end flavors. NMOS devices, at extremely high levels of total ionizing doses, are indeed more radiation tolerant with respect to the PMOS counterpart for the 65 nm technology adopted in the design of the Linear front-end. It can be easily shown that the threshold variation, .Qth , referred to the preamplifier input, in response to a change .Itrim of the tuning DAC output is given by Gaioni et al. [14]: Qth =

.

Itrim 1 . Gm GQ

(32)

The dynamic range of the tuning DAC is set by the .ILDAC current, mirrored in the pixel cells from the matrix periphery. The partial re-design implemented in the RD53B version of the TDAC, was driven by tuning issues emerged, in specific conditions, during the test campaign on the RD53A demonstrator. Specifically, a non-linear TDAC transcharacteristics has been measured for irradiated samples of the RD53A chip operated at temperatures around .−20.◦ C. In these conditions, the TDAC has to be biased with a large .ILDAC current, to compensate for a very large threshold dispersion. However, in the RD53A design, a large TDAC bias current

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Vdd

M6

Unit Cell

Vb1 Vb2 Vdd M5

Ma1 Vb1 Vb2 Vdd

ILDAC

Unit cell x8

Vb1 Vb2 Vdd

Unit cell x4

Vb1 Vb2 Vdd

Unit cell x2

Vb1 Vb2 Vdd

Ma2

Unit cell

Mb

Bi

out

Bi

out

Bi

out

Bi

out Bi

out

VX B3

B2

B1

Itrim

B0 M2

M4

M1

M3

Fig. 5 Block diagram of the threshold tuning DAC included in the RD53A front-end

generates a voltage .VX at the drain of .M2 that is sufficient to drive switch transistors out of the triode region. On the other hand, the removal of cascode structures in the RD53B design guarantees the operation of the switches in the triode region for an extend range of .ILDAC values. Moreover, additional readout logic was added in the RD53B pixel cell thanks to the more compact TDAC layout.

3 Test Results In preparation for the June 2021 submission of the CMS pixel readout ASIC (the pre-production chip), a small prototype integrating the RD53A and RD53B versions of the Linear front-end has been submitted and tested. The prototype, referred to as FELin chip, has been characterized both before and after exposure to TIDs of X-rays up to 1 Grad(SiO.2 ). The prototype chip is briefly described and the key findings of the testing activities are covered in the following sections.

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Vb Vb

Vdd

Unit cell x16 ILDAC

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out

Vb

Vdd

Unit cell x8 Bi

out

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Unit cell x4 Bi

out

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out

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Vdd

Vdd Ma

Unit cell Bi

Mb

out

Bi

out

Vx

B4

B3

B2

B1

Itrim

B0 M1

M2

Fig. 6 Block diagram of the threshold tuning DAC included in the RD53B front-end

3.1 The FELin Chip The FELin chip, shown in Fig. 7, integrates a matrix of 16.×16 readout channels featuring a pitch of 50 .× 50 .μm. The basic brick of the matrix is a single structure of 2.×2 channels laid out in such a way to have a central analog region, surrounded by the digital logic. This is the so-called “analog island” structure already adopted in the design of the RD53A demonstrator. The matrix is split in two 8.×16 submatrices, featuring the two versions of the Linear front-end. The readout chain is equipped with a calibration circuit, which includes a 8.5 fF injection capacitance, providing configurable test signals at the preamplifier input. Such a node is also connected to a pad, featuring the same size of the one integrated in the final CMS readout chip, for sensor bump bonding. Two capacitors of 50 and 100 fF, emulating the presence of an actual sensor, can be selectively switched to the preamplifier input and allow for four possible setups (namely 0, 50, 100 and 150 fF). A programmable switch may also be used to connect the preamplifier input to a detector leakage emulating circuit, implemented by means of an NMOS current mirror. Different samples of the FELin chip were tested before and after exposure to radiation, with TIDs up to 1 Grad(SiO.2 ), by means of an FPGA-based setup and a LabView data acquisition system. The main test results are presented in the following subsections.

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Fig. 7 Microphotograph of the FELin chip, which integrates a 16 .× 16 matrix with RD53A and RD53B front-end channels

3.2 Results Before Irradiation The front-end noise performance has been evaluated in terms of equivalent noise charge, which has been measured by means of charge scans on the readout channels, along with threshold data. During a charge scan, the front-end input signal, .Qin , is made to change within a suitable range, and the comparator hit efficiency is measured. The function .ηc , which is defined as    Qin − μ 1 1 + erf , .ηc = √ 2 2σ

(33)

may be used to fit the efficiency curves. The front-end threshold and equivalent noise charge are represented by the fitting parameters .μ and .σ , respectively. As an example, Fig. 8 shows the efficiency curves (commonly referred to as s-curves) acquired on the sub-matrix featuring the RD53B version of the front-end. The data shown in the plot was obtained at room temperature after the fine-tuning of the threshold to a level close to 1100 electrons, with a 50 fF capacitance shunting the CSA input. From the fitting of such a family of curves, the data shown in Figs. 9 and 10 were obtained. In particular, the histogram in Fig. 9 shows the threshold distribution for the RD53B matrix, with a mean value close to 1125 electrons and a standard deviation, referred to as threshold dispersion, around 29

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Comparator hit efficiency

1

0.8

0.6

0.4

0.2

0

-0.2 0

500

1000

1500

2000

-

Input charge [e ]

Fig. 8 Measured s-curves as obtained for the RD53B Linear front-end after threshold tuning at around 1100 electrons. The s-curves are subsequently fitted with erf function to compute ENC and threshold

electrons r.m.s. On the other hand, Fig. 10 shows the ENC distribution, with a mean value close to 80 electrons r.m.s. Figure 11 shows the mean ENC for different values of the detector capacitor, .CD , for the two versions of the front-end, with the height of the error bars being equal to 1 standard deviation. The equivalent noise charge lies in a range between 60 electrons r.m.s., with no capacitors connected to the preamplifier input, and 130 electrons r.m.s. for .CD equal to 150 fF. For a detector capacitance of 50 fF, compatible to the 3D sensors that are planned to be used in the innermost layer of the CMS tracker, a noise close to 85 electrons r.m.s. was measured for both the flavours of the Linear front-end. Figure 12 shows the ENC for a detector leakage current varying between 0 and 20 nA. As discussed in section II.B, the larger the detector leakage, the larger the .gmp /gmn ratio in (20), which results in an increased equivalent noise charge, as shown in the figure. The ENC increase was found to be somewhat smaller in the RD53B flavour. The time-walk improvement brought about by the RD53B design is clearly visible in Fig. 13, where the time-walk is shown as a function of an input charge, .Qin , ranging from 1150 electrons (i.e. the threshold level) to 1600 electrons. Specifically, for the unirradiated sample which has been tested, the RD53B flavor yielded a time-walk

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40 35

-

μ = 1125.3 e σ = 29.29 e r.m.s.

30

Counts

25 20 15 10 5 0 1000

1050

1100

1150

1200

1250

1300

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Threshold [e ] Fig. 9 Threshold distribution (solid blue), and its fitting (dashed red), for the RD53B Linear frontend operated at a threshold close to 1100 electrons, with a detector emulating capacitor of 50 fF. The plot also reports threshold mean and standard deviation, known as threshold dispersion

of 22 ns, whereas around 33 ns were measured for the RD53A version of the frontend. A smaller time-walk dispersion was detected for the RD53B version: this is compatible with a reduced time constant .τc,cl (discussed in section II.C), which  , triggering the comparator output translates in a faster rising edge of the signal, .Vo,c inverters. The behaviour of the Time-over-Treshold is shown in Fig. 14, again, for .Qin ranging from the threshold level up to 30,000 electrons. According to the RD53 requirements, the bias current, .IK , in the Krummenacher feedback network was tuned in such a way to convert 6000 electrons input signal into a ToT of about 130 ns. A linear response has been measured for both the analog processors for an input charge larger than 2000 electrons, with similar ToT dispersions. The improvement in the threshold tuning capabilities associated with the RD53B design is visible in Fig. 15. The plot shows the tuning DAC dynamic range for the two front-ends, measured at a temperature around .−20.◦ C, as a function of the .ILDAC current. The dynamic range is expected to increase almost linearly with such a current: this is actually the case of the RD53B front-end, whereas a non-linear behavior was detected for the RD53A one, with a dynamic range saturating to a value close to 1700 electrons.

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3.3 Results After Irradiation In order to evaluate the radiation hardness of the RD53A and RD53B Linear frontends, one sample of the FELin chip has been exposed to TIDs up to 1 Grad(SiO.2 ) of X-rays. A Seifert RP149 machine was used to irradiate the prototype chip at the CERN EP-ESE facility, with a temperature that was kept close to .−10.◦ C, and a dose rate of 11 Mrad(SiO.2 )/h. During irradiation, simple charge scans were continuously running to generate analog and digital activities in the chip. The matrix was biased with the default settings before the irradiation, with a threshold close to 1000 electrons. During the irradiation, the bias conditions were not changed, while a fine-tuning of the threshold has been performed at each stage of the irradiation process. The ENC as a function of the TID is shown in Fig. 16, for an emulated detector capacitance of 50 fF. Noise was also measured after 1 day annealing at room temperature at the end of the irradiation campaign. As shown in the plot, radiation has a little impact on the noise properties of the front-end, with moderate

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increases (close to 12 and 6% for RD53A and RD53B, respectively) of the ENC at 1 Grad(SiO.2 ). It is worth noticing that ENC data, here, is relevant to a chip not connected to a sensor. The expected increase of the detector leakage current with the TID, would actually translate in a more pronounced increase in the front-end ENC. A partial recover in the ENC after annealing may be expected: nonetheless, the variation of the measured ENC after 1 day annealing is not significant. This may be explained considering that the measure of the noise after annealing was performed at room temperature, whereas the ENC data during irradiation was gathered at .−10.◦ C. Figure 17 shows the threshold dispersion of the front-ends as a function of the total ionizing dose. The plot shows the data as obtained before (un-tuned) and after (tuned) the fine-tuning of the threshold. It is worth noticing that the tuned-threshold dispersion is roughly a factor of 2 smaller for the RD53B front-end, which features an extra TDAC trimming bit, compared to the RD53A counterpart. The tuned threshold dispersion for the RD53B flavour turns out to be close to 30 electrons

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Fig. 12 Equivalent noise charge as a function of the detector leakage current for the RD53A and RD53B version of the Linear front-end. The ENC is measured for a detector capacitance of 50 fF. The height of the error bars is equal to 1 standard deviations

r.m.s. up to a TID of 400 Mrad(SiO.2 ). A moderate increase is detected in the range 400 Mrad(SiO.2 )–1 Grad(SiO.2 ). A key figure of merit of the front-end, hereafter referred to as .ρ, is the quadrature sum of the tuned-threshold dispersion and the ENC. According to RD53 specifications [12], such a parameter should be smaller than 126 electrons r.m.s. in order not to exceed a noise occupancy level of 10.−6 . Figure 18 shows .ρ as a function of TID for the two versions of the front-end. Notice that RD53A analog processor breaks the 10.−6 limit for TIDs larger than around 200 Mrad(SiO.2 ), whereas the curve relevant to the RD53B one lays always below such a limit. The time-walk for the two front-end flavours, as measured for an input signal close the threshold, is shown in Fig. 19 as a function of the TID. Such a parameter is, in general, significantly smaller for the RD53B front-end, which features a timewalk around 22 ns before irradiation, with a marginal increase for TIDs larger than 200 Mrad(SiO.2 ). The time-walk slightly exceeds the 25 ns limit for TIDs approaching 1 Grad(SiO.2 ). On the other hand, the time-walk measured for the RD53A analog processor, is always well above 25 ns, with a maximum around 45 ns

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achieved at 1 Grad(SiO.2 ). A partial recovery was detected, for both the front-ends, after 1 day annealing at room temperature. A general conclusion which is possible to draw after discussing the performance before and after irradiation of the FELin chip, is that the effects of the radiation on the behaviour of the RD53B Linear front-end are pretty limited. This is actually in line with the radiation tolerance properties of the 65 nm technology [15, 16] which was used for the design of the chip.

4 Conclusions The CERN RD53 collaboration is designing pixel readout chips for the phaseII upgrades of the CMS and ATLAS. In 2017, the collaboration submitted the large-scale chip, called RD53A, including three versions of the analog front-end, referred to as Synchronous, Linear and Differential front-ends. After an intensive

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test campaign on the three readout channels, the Linear analog processor has been selected for the integration into the production chip for the CMS pixels. In preparation to the submission of the pre-production (RD53B) and production (RD53C) chips, a small prototype ASIC, including the RD53A and RD53B version of the Linear front-end, has been fabricated and tested. The paper described the architecture of the Linear front-end and highlighted the design improvements that have been implemented in the RD53B flavour. The test of a prototype chip, integrating a matrix of 16 .× 16 pixels with RD53A and RD53B readout channels, was successful, and very encouraging results were obtained for the RD53B Linear front-end, even for TIDs up to 1 Grad(SiO.2 ). The characterization of the CMS pre-production chip is now in progress in the framework of the RD53 collaboration, with very promising results, and the submission of the CMS RD53C chip is foreseen for mid 2023.

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Acknowledgments The authors would like to acknowledge the valuable assistance of Giulio Borghello during the CERN irradiation campaign. They also like to thank the RD53 members for their support during the design and testing phase of the chip described in the paper. The authors are in debt with Giulio Dellacasa, Natale Demaria, Sara Garbolino and Francesco Rotondo, from INFN Torino, who took care of the integration of the FELin chip and of the development of the data acquisition system.

References 1. Rossi, A., et al. (2022). The CMS tracker for the high luminosity LHC. Nuclear Instruments and Methods, 1048, 167950. 2. Calderini, G., et al. (2022). The ATLAS ITk detector for high luminosity LHC upgrade. Nuclear Instruments and Methods, 1040, 167048. 3. Steinbrück, G., et al. (2020). Development of planar pixel sensors for the CMS inner tracker at the high-luminosity LHC. Nuclear Instruments and Methods, 978, 164438. 4. Meschini, M., et al. (2020). Radiation resistant innovative 3D pixel sensors for the CMS upgrade at the high luminosity LHC. Nuclear Instruments and Methods, 978, 164429. 5. RD53 Web Site. http://rd53.web.cern.ch/rd53/ 6. Marconi, S., et al. (2019). Design implementation and test results of the RD53A, a 65 nm large scale chip for next generation pixel detectors at the HL-LHC. In 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference Proceedings, 18973028. 7. The Tracker Group of the CMS Collaboration. (2021). Comparative evaluation of analogue front-end designs for the CMS inner tracker at the high luminosity LHC. Journal of Instrumentation, 16, P12014.

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8. Gaioni, L., et al. (2021). Optimization of the 65-nm CMOS linear front-end circuit for the CMS pixel readout at the HL-LHC. IEEE Transactions on Nuclear Science, 68(11), 2682–2692. 9. Krummenacher, F. (1991). Pixel detectors with local intelligence: an IC designer point of view. Nuclear Instruments and Methods, 305(3), 527–532. 10. Tsividis, Y. P. (1999). Operation and modeling of the MOS transistor (2nd ed.). New York: McGraw-Hill. 11. Träff, H. (1992). Novel approach to high speed CMOS current comparators. Electronics Letters, 28(3), 310–312. https://doi.org/10.1049/el:19920192 12. RD53A integrated circuit specifications. https://cds.cern.ch/record/2113263/files/RD53A_ specs_V3_2.pdf 13. Pelgrom, M., et al. (1989). Matching properties of MOS transistors. IEEE Journal of SolidState Circ, 24(2), 1433–1439. 14. Gaioni, L., et al. (2020). Threshold tuning DACs for pixel readout chips at the high luminosity LHC. Nuclear Instruments and Methods, 969, 164025. 15. Krohn, M., et al. (2015). Radiation tolerance of 65 nm CMOS transistors. Journal of Instrumentation, 10, P12007. 16. Borghello, G., et al. (2021). Ionizing radiation damage in 65 nm CMOS technology: influence of geometry, bias and temperature at ultra-high doses. Microelectronics Reliability, 116, 114016.

A Readout Electronic System for a 3D Position-Sensitive CdZnTe Gamma-Ray Spectrometer Based on the CPRE10-32 Readout ASIC Tianze Chen, Xiaohui Li, Ke Wang, CunFeng Wei, Lei Shuai, Xiaopan Jiang, Na Wang, Mian Wang, and Long Wei

1 Introduction Semiconductor detectors are widely used in X-ray and γ-ray detection. Among a series of semiconductor materials, the most commonly used materials are Si, Ge, GaAs, HgI2 , CdZnTe, et al. Due to the physical properties of CdZnTe, nuclear detection and imaging instruments based on CdZnTe (CZT) detectors have been used in the fields of homeland security, medical imaging, astronomical observations, and physical research. The research on the CZT began from the 1990s and has achieved many efforts. CZT is a semiconductor material with an average atomic number of 49.1 and a density of 5.78 g/cm3 , which makes it good for blocking X-ray and gamma rays. The band gap of CZT is 1.57 eV, which leads to a high electrical resistivity up to1010  cm.Extensive researches on CZT detectors have led to different types of detectors being designed, among which pixelated detectors are widely used due to the high

T. Chen · C. Wei · M. Wang · L. Wei () Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing, China Jinan Laboratory of Applied Nuclear Science, Jinan, China e-mail: [email protected] X. Li · L. Shuai · X. Jiang Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Jinan Laboratory of Applied Nuclear Science, Jinan, China K. Wang · N. Wang Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China State Key Laboratory of Particle Detection and Electronics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_8

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energy resolution and the capability of acquiring the depth of interaction. To acquire a better energy resolution, He et al. [1] proposed the concept of the 3-D positionsensitive CZT (3D-CZT) detector. The depth of interaction (DOI) information of the case inside the detector is the important information which we should focus on. There are two methods to perform depth measurements: cathode/anode ratio for single interaction events [2] and electron drift time for multiple interaction events [3]. By acquiring energy and depth data, the energy resolution is improved through 3-D corrections. Meanwhile, the energy and depth information make it possible to implement Compton scatter imaging with a single pixelated detector [4]. In recent years, Kromek, Redlen and, other companies have focused their attention on the growth of CZT materials and the production of detectors. The ASIC chips, which are used in 3D-CZT detectors, include VASTAT from IDEAS [5] and H3D from Brookhaven National Laboratory [6] and so on. Based on a CPRE10-32 readout application specific integrated circuit (ASIC) [7], we designed a readout electronic system which is used for 3D-CZT detectors. This work also includes some researches on the way to achieve a better electronic noise performance. It is the first time to use and verify the new CPRE10-32 ASIC. This work is a prototype of the Compton imaging system of which every part is designed by ourselves, and it can be updated according to our demands. The result of the experiment could also become the references for other related designs. Experiment results of energy and time information demonstrate that the readout electronic system can meet the needs of Compton imaging. The experiment of Compton scatter imaging shows that the system has the ability to realize the Compton imaging. The three main parts of the readout electronic system include hardware basics, FPGA firmware and PC software. The depth correction using the depth of interaction is included in the PC software. This work is a complete system foundation for the Compton scatter imaging. More research would be conducted based on this readout electronic system.

2 Compton Scatter Imaging Using 3D-CZT A schematic of the 3D-CZT detector and the typical Compton scattering case inside the detector is shown in Fig. 1. A normal Compton scattering event will cause two interactions inside the detector, whose energy will be absorbed by two pixels in most situations. By using energy E1 and E2 of two pixels, the Compton scattering angle can be calculated. Then the conical surface can be determined in 3D space using the angle and the interaction depth Z1 and Z2 of two pixels. The Compton image can be reconstructed through multiple conical surfaces. The Compton energies and scattering angle are related as in Eqs. (1 and 2). E0 = E1 + E2

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3 Depth of Interaction 3.1 C/A Ratio The type of the 3D-CZT detector mostly used is the Single-polarity charge sensing detector. The depth of interaction can be obtained by acquiring the signals from the cathode and the anode for each gamma-ray event. The weighting potentials of these two kinds of electrodes are different. According to the Shockley–Ramo theorem, the signals of the cathode and the anode can be related to Eqs. (3 and 4), where the e0 is the charge of electron and the Z is the distance off the anode. Qcathode = N e0 ∗ Z

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Therefore, the C/A ratio can be calculated, and the result is Z. This result shows that the depth of interaction only depends on the signal of the cathode and the anode. Although there are some differences between theory and the reality, it can still provide the way to determine the depth of interaction z that it is related to the C/A ratio. The only problem is that the C/A ratio cannot be used in Compton Scatter Imaging.

3.2 Electron Drift Time When there is more than one pixel motivated in the array, the C/A ratio cannot obtain the depth of interaction any more. As the Compton scatter imaging is the final purpose, a typical Compton scattering case would be discussed here which is shown in Fig. 2. Assuming that the electron would drift at a constant velocity inside the detector, the drift time can represent the depth of interaction. The cathode is always the first to trigger the readout electronics, then followed by the two anodes. Using the fast-shaping circuit, we will get two data of time Ta and Tb which are shown in Fig. 3. The functional relationship between electron drift time T and the depth of interaction Z can be obtained by calibration. It is possible for us to acquire the depth data by obtain the electron drift time data in multiple-pixels interaction cases.

Fig. 2 Schematic illustration of the Compton scattering case

Fig. 3 The trigger of the cathode would be the first followed by the other two. These two periods of time data would be acquired using the ASIC

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4 Introduction of CPRE10-32 Readout Chip CPRE10-32 is a 32-channel general-purpose readout chip designed for particle detector pulse signal readout, and is the latest in the CPRE series. The energy information and time information can be readout with low noise and low power consumption. The original magnification of the chip is suitable for Si-PIN, CZT, and other semiconductor particle detectors which have no multiplication effect. By using a smaller gain in the chip or an external charge distribution structure, it can also be used for Multi-anode Photo Multiplier Tube (MaPMT), Gas Electron Multiplier (GEM), and other detectors with a larger gain compared to semiconductor particle detectors. There is an independent test signal chain from a pin to the input of every channel inside the chip so that the function and characteristic can be tested without an actual signal. Table 1 presents some performance characteristics of CPRE10-32. The functional block diagram of single readout channel is shown in Fig. 4. Table 1 Performance characteristics of the CPRE10-32 Die

Parameter Technology Size of DIE Number of pins Number of channels Input noise Polarity Time resolution Power consumption Counting rate Mode of signal output Working temperature

Characteristics 0.35 μm CMOS 7100 × 8500μmm2 123 32 200 e− ± 22 e− /pF Positive and negative optional About 10 ns 5 mW/channel and 160 mW overall Maximum 100 k/s Single-end and differential selectable −20~80 ◦ C

Fig. 4 Functional block diagram of single readout channel

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The CPRE10-32 chip has multiple functions to control most parts of the circuit. The programmable parameters include the switch of each channel, the size of the feedback capacitor, the DAC threshold voltage of slow and fast shaping circuits and the gain number. With the help of these parameters, it is possible for us to select the suitable parameters in different conditions of experiments.

5 The Design of the Readout Electronic System Based on the physical theory of the Compton scattering image, the requirements of the readout electronic system are shown as follows: 1. The system should provide working conditions for the 3D-CZT detector including high voltage (−1000 V to −2000 V) and six low-noise power rails for the ASIC and the connection between ASIC and FPGA. A high-speed cable of Samtec is chosen to transport control digital signals, power supplies and analog output of ASIC. 2. The system should have a good electronic design in linear response and electronic noise to achieve reliable data of 3D-CZT detector. 3. The system should have the ability to acquire the energy and time data of the 3DCZT detector. Time data will be used to calculate the depth data by electron drift time. The goal of the energy resolution is lower than 1% at 662 keV of Cs-137 using the depth correction. (The original energy resolution of CZT is normally about 1.23 keV (0.18%) at 662 keV of Cs-137.) 4. The system should realize full duplex communication between PC and FPGA to monitor and control the system conveniently. The Gigabit network is used to connect FPGA and PC. 5. The system would save the data acquired by the ASIC in PC and display the original energy spectrum on the GUI. Data processing is temporarily offline. When the processing algorithm is determined in the future research, the processing would be online in the PC software and more figures would display on the GUI. We designed a complete readout electronic system based on the CPRE10-32 readout chip to meet the requirements. It is composed of FEE board, DAQ board, the logic firmware of FPGA, and the PC software on host computer. The FEE board works in a shielding case.

5.1 The Hardware Architecture Design of the Readout Electronic System We use a design in which the FEE board containing the ASIC chip is separated from the DAQ board containing the FPGA chip. The two boards are connected through

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Fig. 5 Hardware architecture design of the readout electronic system

Fig. 6 Picture of the FEE board and DAQ board. The CPRE10-32 chip is wire-boned to the PCB

connecting wires. By doing so, the interference between the digital part and the analog part of the FEE can be reduced. The hardware architecture design of the readout electronic system is mainly divided into two parts: 1. FEE board, including CZT detector connector, CPRE10-32 chip and high voltage input connector; 2. DAQ board, including FPGA chip, FPGA power supply chip, FEE power supply chip, ADC chip, Gigabit network chip, and high voltage module. The architecture design is shown in Fig. 5. A picture of the FEE board and the DAQ board is shown in Fig. 6.

5.2 FPGA Control Logic Based on the readout electronic hardware designed above, ASIC chips, FPGA chips, high-voltage modules, and their control and monitoring are required. The system

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Fig. 7 Block diagram of the firmware logic function modules

includes all the classic control and monitoring functions required in a readout board. The four main functions performed by the FPGA board are: 1. The communication between the FPGA and PC using a Gigabit Ethernet for the transmission of control instructions and the upload of data; 2. Parameters’ configuration of ASIC and the control of working status; 3. Storage, selection, and packaging of data acquired through ASIC; 4. The configuration and monitoring of the high-voltage module. To realize the requirements of the logic functions, we adopt a modular design, which can separate the requirements to modules. Every module can be tested and modified individually. The FPGA used in this article is the Artix-7 series FPGA of Xilinx Company, whereby the Vivado 2022.1 software platform of Xilinx Company is used in the firmware logic development. The programming language used is Verilog-HDL. A design block diagram of the firmware logic function modules is shown in Fig. 7. In the control logic, the functional modules that play an important role are the instruction decoding module, the ASIC control module, the high-voltage control and monitoring module, the data cache packing module, and the Ethernet module. With the help of all above modules, the host computer can directly change the configuration parameters of the ASIC, and can freely control the start and end of data acquisition, while obtaining the data collected by the ASIC in real time.

5.3 Design of PC Software To cooperate with the control logic of the FPGA, it is necessary to design a PC software on the host computer which can communicate with the FPGA and

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Fig. 8 Design block diagram and GUI interface of the PC software. The most important functions are the ASIC configuration and Data receiver and display

implement functions to send configuration data, receive and display collected data, and save it locally. The PC software is designed based on the C++ QT open-source library. To distribute and change configuration parameters more conveniently, it is necessary that the energy data of each channel can be recorded in real-time and displayed in the form of an energy spectrum. Moreover, it is necessary for the GUI to show the data of the high voltage and counting rate of every channel; thus, the PC software is developed. A design block diagram and GUI interface of the upper computer are shown in Fig. 8.

6 System Characterization of the Readout Electronic System After the hardware and software design of the readout electronic system is complete, a system characterization is required. Characterizations included baseline and noise, and linear response and dynamic range. These characterizations can directly reflect the performance of the readout electronic system, and provide basic data for subsequent experiments.

6.1 Noise Characterization of the Readout Electronic System In this experiment, the electronic noise was tested under the conditions of no detector and no high voltage, and connecting a detector with high voltage, respectively. To test the electronic noise of the system without the detector, a signal generator was used to generate a standard signal, which was set to 50 mV and 500 Hz. The system was designed for CZT detector so that we used the ENN to show the characterization of the system. The average ionization energy of CZT used here is 5 eV. Because the CPRE10-32 chip had a test pin which was connected with the input of channel inside the chip through a capacitor, the test signal could be connected to the test pin directly. In order to study the influence of the gain of the ASIC chip on the noise simultaneously, we used the minimum gain and maximum

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Fig. 9 ENN of the readout electronic system without the detector when the minimum and maximum gains are selected under the condition of using a standard signal

Fig. 10 Baseline and its noise while connecting a detector and high voltage. The minimum gain is selected. Channel 1 is connected to the cathode, and other channels are connected to the anode. The baselines of the two electrodes are different

gain to conduct the noise test. The results are shown in Fig. 9. The electronic noise when the system is connected with the detector and the high voltage is applied, is called “baseline noise” here. The data of this noise would provide the information for further experiments on noise analysis. According to the data acquired, the ENN of the electronic noise can be calculated. The results are shown in Fig. 10. As the reason that it was first time to use and test the CPRE10-32 ASIC, we decided to do some extra experiments on the influence of the design of electronic board on the electronic noise. The ground copper under the tracker between detector and ASIC had two ways to design, whether to remove or keep. The ground copper under channel 0–24 were removed, and the ground copper under channel 25–31 were kept. We did not know which kind of design would have better electronic noise performance in our system because we had found both designs in other works using ASIC and detectors. The channel 15 and 28 were bad at the pin pad. So, these two channels were float pins. The channel 0 was connected to an individual connector to test the function of the ASIC. It could be found from the Figs. 9 and 10 that the ENN of channel 25–31 were larger than that of channel 1–24, which proved

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Fig. 11 The real-time energy spectrum while changing the input signal voltage from 50 mV in the experiment. The x-axis represents ADC counts and y-axis represents counts. The spectrum data collected by the system increases nearly at equal intervals with the increase of the input signal

that removing the ground copper had better noise performance. The electronic noise increased after connecting the detector probably because of the noise of high voltage and the increase of the crosstalk between channels. This result provided a reference for our future electronic design. When the system is not connected with the detector, the ENN is about 265 e− at minimum and maximum gain, and the electronic noise is approximately 3.335 keV at minimum gain and 3.074 keV at maximum gain. The data of the electronic noise is the FWHM of the electronic noise which is used to calculate the ENN. After connecting the 3D-CZT detector and high voltage, the ENN is about 375 e− , and the baseline noise is approximately 4.72 keV.

6.2 Linear Response and Dynamic Range of the Electronic System In this part of experiment, the standard signal input was used to drive the electronic system. The data output from the ADC which was acquired by the FPGA was used as the standard to analyze the linear response characteristics of the readout electronic system to the input signal. The input signal ranges from 50 mV to 1000 mV in steps of 50 mV until the electronic system is saturated. There is a 75 fC capacitor inside the ASIC right after the input signal. So, the input signal would be transformed into the signal of electric charge. The real-time energy spectrum acquired in the experiment while changing the input signal is shown in Fig. 11. The response curve of the read amplitude data with respect to the input signal is shown in Fig. 12.

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Fig. 12 (a) Response curve of data and signal of channel 10. The Pearson’s r and Linearity γ are shown in the figure. (b) Response curve of data and signal of channel 1–31 Fig. 13 Response curve of data and signal of channel 10 with smaller step size

According to the results of the experiments above, the Pearson’s r is about 0.9991 and the linearity γ is about 1.36%. The Integral Nonlinearity (INL) and Differential Nonlinearity (DNL) of the system is about 115 ADC counts and 0.52 ADC counts. The linear response characteristics of the system are good enough for the energy detection. The response is nonlinear when the input signal is extremely large, which would not appear in most usage scenarios. In order to evaluate the dynamic range of the system, we conducted a more accurate test of the transition between the linear and nonlinear regions of the system response to find the linear region and the absolute dynamic range. By using a signal generator and using a smaller step size to test at the minimum gain, the linear range of the readout electronics could be obtained. The test results are shown in Fig. 13. It can be determined from the results that the absolute dynamic range of the electronic system designed in this paper was approximately 0–9145 ADC counts, and the linear dynamic range was approximately 0–8556 ADC counts. The baseline had been subtracted from both ranges. According to the energy data of the radioactive source, the dynamic range of the linear range was approximately

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0–450 keV at the maximum gain, and the dynamic range of the linear range was approximately 0–3 MeV at the minimum gain. The minimum energy depends on the experimental environment and trigger threshold and the choice of gain number. The minimum energy of different channels is also different. Therefore, in order to make it equivalent for every channel, 0 keV was used as the baseline reference, and the actual value was greater than 0. For example, the dynamic range of channel 10 was approximately 20–450 keV under the condition of maximum gain. When the minimum gain is selected, the dynamic range of channel 10 was approximately 100–3 MeV.

7 Functional and Performance Characterization Using 3D-CZT Detectors The 3D-CZT detector used in this experiment was an 11 × 11 array. The size of the detector was 22 × 22 × 5 mm. The high voltage is selected as −600 V at the cathode. Considering that this is a prototype and this is also the first time using the CPRE10-32 chip, we chose to use one CPRE10-32 chip to verify functionality and test performance. Thirty channels were selected to connect the detector in the actual design. One channel was connected to the cathode signal terminal. The others were connected to the anode signal terminal. After testing, it was found that channel 15 and channel 28 did not work properly due to wire-bonding problems. Two radioactive sources, Am-241 and Cs-137, were used in the experiment. They were placed 2 cm away from the cathode of the detector. The data collection time ranged from 2 to 8 h. The temperature was around 20 ◦ C. The experimental environment is shown in Fig. 14.

Fig. 14 Picture of Experimental environment

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Fig. 15 The energy spectra of Am-241 at the maximum gain. Due to the noise problem, the data of 8 channels could not be acquired correctly, so it is not shown here

7.1 Spectral Test Using Radioactive Sources Two radioactive sources, Am-241 and Cs-137, were used to conduct data acquisition tests. Without selecting hit cases, the baseline was subtracted from the energy spectrum information. The energy spectrum diagrams are shown in Figs. 15 and 16. According to the energy spectrum test, it can be found that the FWHM for the full-energy peak of Am-241 at 59.6 keV under the maximum gain was preferably 7.25% for 14 channels. The FWHM of the full-energy peak of Cs-137 at 662 keV was preferably 2.22% for channel 11 at low gain. The energy spectra of the last 6 channels in Fig. 16 were greatly disturbed. The noise of these channels, as shown in Fig. 15, was too large and could not be read normally, so the energy spectra were not displayed. This phenomenon was also found in the noise test above.

7.2 Electron Drift Time and Depth Correction Depth information can be obtained by recording the voltage as a function of time. Since the design uses only one ASIC chip and only 30 channels are connected, the data of 121 channels cannot be completely read out, and therefore we only selected

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Fig. 16 The energy spectra of Cs-137 detected by 28 anode channels at low gain

the single-anode signal triggering case, i.e., the case in which one anode and one cathode were triggered simultaneously was acquired. Given that it is impossible to determine whether other channels that are not connected are triggered, depth correction using the C/A ratio method cannot be performed smoothly. Therefore, we tried depth correction based on electron drift time. After obtaining the time information, depth correction of the energy spectrum was conducted according to the correction method mentioned above. The energy data of Cs-137 at different depths of channel 12 were separated, as shown in Fig. 17. Through depth correction, the FWHM of the 662 keV full-energy peak was improved from 1.35% to 0.76% at medium gain and 3.08% to 2.51% at low gain, respectively. The results are shown in Fig. 18. The correction parameters of this result were then used to directly correct the newly acquired energy spectrum, of which the FWHM was successfully improved from 2.05% to 1.54%, as shown in Fig. 19. The experiment demonstrates that the depth correction was conducted correctly, while also highlighting that the readout electronics designed in this experiment can simultaneously collect energy and time information, which meets the requirements of Compton scattering imaging of 3D-CZT. In Fig. 18, the scattering part almost disappears at low gain, which is related to the relatively high threshold and small signal amplitude. The energy shown here must trigger slow and fast shaping triggers at the same time, and the output of slow and fast shaping circuit are not the same. The output of the fast-shaping circuit is smaller than that of the slow-shaping circuit, which would cause the situation that the slow trigger is triggered and the fast trigger is not triggered. Meanwhile, the

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Fig. 17 Energy spectra of Cs-137 obtained from channel 12 at different depths

Fig. 18 The energy spectra of channel 12 before and after correction, where the left picture is medium gain, and the right picture is low gain

energy threshold of the minimum gain which would cause trigger is larger than that of the medium gain. Considering all these conditions, the data in scattering part would be thrown away and will lead to this kind of energy spectra. This situation provides a reference for us to choose the appropriate gain number. So, we choose to exhibit this result.

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Fig. 19 Results after directly using the correction result under low gain to correct the newly obtained data. The effect is consistent with the calculation group in Fig. 18 right

8 The Design of a Four-Chip Readout Electronic System After the verification and the test of the one-chip system, the basic function of the system has been achieved. But if we want to conduct more experiment on 3DCZT detector or on the spectral correction algorithm, the one-chip system which cannot collect all channels of the 3D-CZT detector is not suitable. Therefore, we designed a four-chip system to gain the full function of the 121 channels of the 3D-CZT detector. The DAQ board is the same as that in one-chip system. After the design of the four-chip FEE board, we have conducted more experiments on the characterization of the depth of interaction of the 3D-CZT detector. The spectral characterization is also performed in this study.

8.1 The Hardware Architecture Design of the Four-Chip System The main design of the four-chip FEE board is the same as the one-chip FEE board. The difference is that the four-chip would have more signal routes to place. The total design of the four-chip FEE board should be paid more attention on the interference between the chips. Figure 20 is the picture of the four-chip FEE board after the design. The area of the four-chip FEE board is much smaller than the one-chip board. The reason is that there is no need for us to do the confirmatory experiment. So, most of the area can be saved to decrease the area of the board. Although the fourchip FEE board shown here is not a minimum area design, it still proves that using the CPRE10-32 ASIC chip can build a small size of imaging devices. If the ASIC could integrate more channels in a single chip, the area used of the FEE board can become smaller and more integrated.

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Fig. 20 The picture of the four-chip FEE board. The chips are also wire-boned to the PCB

8.2 Spectral Test Using Radioactive Sources After the design of the four-chip FEE board, we conducted the spectral test. Using the CPRE10-32 ASIC chip, we have a lot of configuration parameters to choose which include the threshold DAC parameters, the gain parameters, the shaping time parameters and so on. A different combination of the configuration parameters could lead to a better performance when the conditions of the environment or the types of the radioactive source are different. Undercertain conditions, including a temperature of 15 ◦ C, a radioactive source of Cs-137, a middle gain and a high voltage of −600 V, a energy spectrum diagram is shown in Fig. 21. The basic energy spectral test shows that the function of the four-chip FEE board was correct. The best energy resolution is 2.59% of the channel 57. The result is a bit higher than the one-chip FEE board. The major reason could be the larger crosstalk from the other signal routes. One chip could also be interfered by other chips when they are working. This study is the prototype of the readout electronic system for the 3D-CZT detector. So, these kinds of interferences are acceptable and would be improved in the future.

8.3 C/A Ratio and Electron Drift Time In the experiments of the four-chip FEE board, the research on the depth of interaction inside the 3D-CZT detector is the most important. The crosstalk and the interferences of the channels could be improved by a new design of the FEE board. But the research on the characterization of the depth of interaction would lead to the next-stage of research on 3D-CZT detector and the Compton scatter imaging.

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Fig. 21 The energy spectrum of the Cs-137

As the discussion above, the C/A ratio can only perform in the single-pixel interaction cases smoothly, and the electron drift time can perform anytime. So, we select the single-pixel interaction cases to research the characterization of the depth of interaction. First, we calculate the C/A ratio of all cases and tag every case with its ratio. By doing this, we can acquire a diagram of the distribution of every case related to the ratio. To find a common result, we choose the channel 61 as the example instead of the best channel 57. The diagram is shown in Fig. 22. The X axis is the C/A ratio and the Y axis is the ADC counts. Every case has its energy information and the C/A ratio information. The ADC count represents the data of energy. It is obvious that the full-energy peak is different at different ratio. This phenomenon would lead to a decline in energy spectrum resolution because the energy spectrum finally used is obtained by stacking cases of these ratio. The ratio from 0 to 1 represents the depth of interaction from anode to cathode. So, the full-energy peak would transform from low to high and decrease from the top uniformly. Our purpose is to achieve a good energy resolution at the full-energy peak. To realize the purpose, we should normalize the ADC counts of the fullenergy peak at different C/A ratio. But before the normalization, it is necessary for us to pay attention to the electron drift time. As the capability of acquiring the time information, we can obtain the electron drift time of every case. We can make

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Fig. 22 The diagram shows the distribution of the cases related to the ratio

Fig. 23 The diagram shows the distribution of the cases related to the electron drift time

the same diagram as the C/A ratio does with replacing the ratio into the electron drift time. The diagram is shown in Fig. 23.

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Fig. 24 The diagram shows the relationship between the C/A ratio and the electron drift time

It can be found from these two diagrams that the shapes of the full-energy peak are similar to each other. But the other parts of the energy spectrum are not the same. As mentioned above, the normalization of the full-energy peak is our purpose. So, we focus on the full-energy peak first. In order to find the relationship between the C/A ratio and the electron drift time, we select the cases of the full-energy peak and draw the diagram of relationship between the C/A ratio and the electron drift time. The result is shown in Fig. 24. The middle part of the diagram can be fitted to a straight line through the origin. The result shows that the electron drift time and the C/A ratio can represent the depth of interaction consistently. The origin represents the anode of the detector. The C/A ratio can not distinguish the cases of which the ratio is below 0.25 or above 0.85 and the electron drift time can not distinguish the cases of which the time is below 250 ns or above 850 ns. We can perform the depth correction now using both the C/A ratio and the electron drift time. The result is shown in Fig. 25. The correction results show that the electron drift time performs a better energy resolution than the C/A ratio does. Although these two kinds of depth correction lead to different results, they are all working properly. According to this research, we could demonstrate that the readout electronic system has the capability to provide the working conditions for the 3D-CZT detector. The depth of interaction of the cases inside the detector can provide information for further study on both the characterization of the CZT detector and the Compton scatter imaging. The actual relationship between the depth of interaction and the C/A ratio or the electron drift

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Fig. 25 The result of the depth correction of the electron drift time and the C/A ratio

Fig. 26 The photo of the environment of the experiment

time is not a straight line. So, extra researches on the function relationship between these parameters should be conducted.

9 The Experiment of Compton Scatter Imaging After all the experiments above, it is able for us to conduct the Compton scatter imaging experiment. Put the detector towards a direction and lay the radioactive source Cs-137 away from the detector. The Fig. 26 shows the environment of the experiment. To realize Compton imaging, the two-pixels events are chosen as the basic data for image reconstruction. The radioactive source Cs-137 has a radioactive activity of 20 μ Ci. So, the distance between the radioactive source and the detector was selected as 25 cm. The Compton scatter imaging results using simple back projection are shown in Fig. 27. The results prove that the readout electronic system has the ability to conduct the Compton imaging and can support other researches in the future.

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Fig. 27 The results of Compton scatter imaging using simple back projection. (a) The radioactive source is 25 cm away from the center of the detector. (b) The radioactive source moves 25 cm towards left from the position in (a)

10 Conclusion Based on a new CPRE10-32 readout ASIC chip, we developed an electronic system used for the 3D-CZT detector. In this chapter, we have introduced the hardware and software design of the system, the results of the functional experiments using radioactive source and the experiment of Compton scatter imaging. After all the experiments have been conducted in this work, the readout electronic system has been proved to be able to work properly connecting the 3D-CZT detector and can perform the Compton scatter imaging. More experiments would be conducted in the future based on this electronic system.

References 1. He, Z., et al. (1999). 3-D position sensitive CdZnTe gamma-ray spectrometers. Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment, 422(1–3), 173–178. 2. Zhong, H., et al. (1996). 1-D position sensitive single carrier semiconductor detectors. Nuclear Instruments and Methods in Physics Research, 380(1-2), 228–231. 3. Zhang, F., et al. (2004). 3D position-sensitive CdZnTe gamma-ray spectrometers: Improved performance with new ASICs. Proceedings of SPIE - The International Society for Optical Engineering, 5540, 135–143. 4. Dan, X., Zhong, H., et al. (2004). 4-pi Compton imaging with single 3D position-sensitive CdZnTe detector. Proceedings of SPIE - The International Society for Optical Engineering, 5540(5540), 144–155. 5. Zhu, Y., & Zhong, H. (2012). Performance of a 2-keV digitizer ASIC for 3-D positionsensitive pixellated semiconductor detectors. In Nuclear science symposium & medical imaging conference IEEE (pp. 4109–4112). 6. Feng, Z., et al. (2012). Characterization of the H3D ASIC readout system and 6.0 cmˆ3 3-D position sensitive CdZnTe detectors. IEEE Transactions on Nuclear Science, 59(1), 236–242. 7. Wang, N., Wang, K., et al. (2016). CPRE low-noise readout chip for semiconductor detectors and the development and application progress of system. In The 18th National annual conference on nuclear electronics and nuclear detection technology.

Space Applications of CdZnTe and CdTe Detector Systems: Past, Present and Future Branden Allen

1 Introduction Here I will attempt to outline some of the significant threads of CdTe and CdZnTe (CZT) detector technology development alongside the parallel evolution in high energy space research, encompassing astrophysics, heliophysics, and planetary science. It is not intended to capture the whole scope of both enterprises, but rather, to provide sufficient detail to enable the interested reader some insight into how these threads have tied together in the past and how current trends might propel the field forward in the years to come.

1.1 Observation Opportunities The advancement of practical technologies and science are complementary and selfsupporting components of the same enterprise and is all the more true for the space sciences. Over the duration of their lifetimes, all observatories operate in remote environments far beyond the reach of direct human intervention. To ensure that science objectives and the operational lifetime required to achieve these goals can be guaranteed with a high degree of certainty, these missions require substantial development and rigorous preflight qualification prior to their deployment in the space environment. The dawn of the space age launched a revolution in our understanding of planetary science, astrophysics and heliophysics. The ability to place payloads above

B. Allen () Harvard College Observatory part of the Center for Astrophysics | Harvard-Smithsonian, Harvard University, Cambridge, MA, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_9

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the Earth’s atmosphere lifted the veil on large sections of the Electromagnetic (EM) spectrum that had previously been denied to space scientists due to atmospheric absorption and scattering. This is particularly true for high-energy astrophysics at energies extending from the extreme UV (EUV) at approximately 10 eV (124 nm) to the soft .γ -ray regime up to about 50 GeV (0.25 fm); above approximately 50 GeV ground observations have been routinely carried out for Very High Energy (VHE) sources using Imaging Atmospheric Air Cherenkov Telescopes (IACTs) (e.g. MAGIC [126], HESS [8], HAWC [7], LHASSO [9], Tibet AS.γ [13], etc.) which are able to indirectly detect astrophysical .γ -rays by measurement of particles and photons produced in km-scale Extensive Air Showers (EASs) that are initiated by a single photon or cosmic-ray. Within the EUV to soft .γ -ray band instruments may be deployed in one of the three following ways: 1. On board high-altitude balloons. NASA currently supports the flight of payloads of up to 3700 kg at altitudes ranging between 30–45 km above mean seal level (MSL) for a duration of up to 2 weeks. More recent advances have enabled the launch of long-duration balloon flights (LDBs) and ultra-long duration balloon flights (ULDBs) with mission lifetimes extending up to approximately 100 days [61]. Additionally, balloon payloads also provide a relatively inexpensive proving ground for the flight-qualification of technologies and instruments which may later be deployed on satellites that are typically about 2 orders of magnitude more costly. 2. Shorter duration observations at higher altitudes than achievable with balloon payloads may be obtained using sub-orbital rockets. Currently, apogees of up to approximately 1600 km and spaceflight durations (greater than 100 km altitude) of up to 1300 s can be achieved [123]. Notably, the whole of X-ray astrophysics was launched with such a rocket on June 18, 1962 at 2359 MST, where, during a 350 s flight the first detection of a soft astrophysical X-ray source was made using a payload consisting of 3 large, collimated, Geiger counters [56]. At present, sub-orbital rockets remain an important tool where short-duration observations are acceptable and are currently most frequently employed for heliophysics and space weather studies. 3. Finally the addition of a flight instrument to a dedicated satellite or, quite commonly, as part of a suite of instruments for the study of a series of well defined science goals is the preferred method, in spite of the cost. Well designed observatories such as Hubble Space Telescope (HST) (launched: 24 April 1990) [27] , Chandra (launched: 23 July 1999 on STS-93) [151] and XRay Multi-Mirror Mission (XMM) Newton (launched: 10 December 1999) [79] have remained operational and productive for 30 to 20 years. With the notable exception of HST (cf. [24]) none of this has been achieved through repair or replacement of any of the components. Incidentally this is the only method available to planetary science which, in addition, must survive a long cruise phase lasting 6 months up to a decade or more before observations may even begin.

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Today all 3 methods are utilized by governments around the world, as well as some private entities, to provide access to space enabling a broad variety of investigations covering a wide array of topics in astrophysics, heliophysics, planetary science, and Earth science. In parallel, the development of new detector technologies has vastly improved the sensitivity and scientific impact of these payloads per unit mass. This is particularly true of CdTe and CdZnTe (CZT) which have been increasingly used in spaceflight over the last 20 years, particularly for astrophysics applications, greatly expanding the reach and impact of investigations in the X/.γ -ray regime.

1.2 High Energy Astrophysics and the Space Age As outlined three key technologies exist to extend the reach or our instrumentation beyond the influence of the Earth’s atmosphere. The oldest of these methods is high-altitude ballooning. Since the first crewed flights began with the Montgolfier brothers hot air balloon demonstration at Versailles in 1783, balloon flights have expanded our view of the world, initially by direct observation, then with photography followed by the addition of increasingly complex instrumentation as new technologies were developed and became available. The initial discovery of cosmic rays in 1912 by Victor Hess was made from a balloon [68] in a series of flights which opened a new line of research into their origin and properties. These studies lead to greater understanding of the space environment and simultaneously helped launch the field of modern fundamental particle physics with Carl Anderson’s discovery of the positron (a.k.a. positive electron) [14] and the discovery of the muon shortly thereafter [14]. In the same period, accelerated development of rocket technologies throughout the interwar period (1920s-1930s), beginning with the flight of the first liquid fueled rocket by Robert Goddard on 16 March 1926 from Auburn, MA and his launch of the first scientific payload, a barometer and camera, in 1929. Additional advances throughout the 1930s and 1940s culminated in the launch of the first rocket outside of the Earth’s atmosphere from the Heeresversuchsanstalt Peenemünde on 20 June 1944 and, simultaneously, increased interest in rocketry within the United States saw the reorientation of the Guggenheim Aeronautical Laboratory of the California Institute of Technology (GALCIT), the forerunner of NASA Jet Propulsion Laboratory (NASA-JPL), toward rocket research in 1938 under Frank Molina. Ultimately GALCIT, under the Ordinance-California Institute of Technology (ORDCIT) program, successfully launched the first exemplar of what may be considered the first sounding rocket, the Wac Corporal, in 1945 marking the start of regular sounding rocket flights and the formation of the first permanent sounding rocket launch facility at the White Sands Proving Grounds. The Wac Corporal is, in many respects, the forerunner of the Aerobee rocket which served

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as the workhorse for the NASA sub-orbital flight program in the decades to follow. Additionally, captured V-2 rockets and components shipped back to the U.S. at the close of the second world war bolstered early sounding rocket experiments and flew a number of notable payloads throughout the late 1940s and 1950s. For a more complete history the interested reader may consult [36] and the references therein. By the 1950s all of the necessary vehicles for the propulsion of scientific payloads into the uppermost reaches of the Earth’s atmosphere and beyond were in place, settings the stage for the deployment of the world’s first scientific space payloads. The first successful X-ray and Extreme Ultraviolet (EUV) observations of the sun were conducted with V-2 Rocket No. 49 [49] on the 29 September 1949 and followed by a slew of other sub-orbital flights with a wide variety of objectives. The launch of Sputnik I on 4 October 1957 marked the beginning of the space age and was quickly followed by the launch of Explorer 1 into Earth orbit with a Jupiter C rocket almost 4 months later on 31 January 1958. Explorer 1 carried with it the first scientific satellite placed into orbit and enabled the discovery of the Van Allen radiation belts [148]. During the 1960s X-ray astronomy was initiated and rapidly advanced through a series of sub-orbital flights until the first dedicated science satellite for the study of astronomical X-ray sources, Small Astronomy Satellite A (SAS-A) or -1 was launched on 12 December 1970 from the San Marco platform, located off the coast of Kenya, by Agenzia Spaziale Italiana (ASI) on behalf of the United States, a first for a US payload. Following launch SAS-A was renamed Uhuru in honor of Kenyan independence achieved just 7 years prior [77]. Uhuru remained in operation until 10 March 1973 and completed the first full survey of the X-ray sky in the 2–20 keV energy band. Following the success of Uhuru a wide variety of payloads were placed into low Earth orbit (LEO) dedicated to the study of X-ray astrophysics. At the same time, the United States Department of Defense (DOD) had initiated the Vela nuclear test-ban monitoring program which consisted of a constellation of 12 satellites launched in pairs at a cadence of approximately 1 per year beginning with the launch of the first pair, Vela 1A and 1B, on 17 October 1963 and ending with the final pair Vela 6A and Vela 6B on 8 April 1970 [102]; just a few months prior to the launch of Uhuru. Although Vela did not definitively identify any test ban violations, they did discover intense bursts of .γ -ray radiation of cosmic origin [86]. Dubbed Gamma-Ray Bursts (GRBs), these events remain a subject of intense study critical to our understanding of the end states of stellar evolution, the history of nucleosynthesis over the lifetime of the universe and serve as a probe of extreme physics during the mergers of any permutation of black holes (BHs), Neutron Stars (NSs) and White Dwarfs (WDs) pairs. The study of GRBs is in fact one of the main use cases for spaceflight CZT and CdTe instruments at present and also was one of the motivating factors for the launch of the first CdTe detectors during the 1970s aboard the ISEE-1 payload.

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1.3 The Search for New Detectors and Early Spaceflight Deployments of CdTe (1970–1990) Around the same time that X-ray astronomy had established a firm footing in LEO, CdTe had begun to gain recognition as a potentially useful medium for the detection of .γ /X-rays. The first suggestions that CdTe could potentially be used as a radiation detector [38] were proven correct within less than a decade, when a handful of groups working to improve CdTe growth techniques for a variety of purposes unrelated to X-ray detector development managed also to demonstrate sensitivity to X/.γ -radiation [10, 155] in 1968 at Hughes Research Laboratories. Meanwhile large efforts to explore the origin of GRBs were launched by astrophysicists and instrumentalists who, recognizing the intrinsic limitations in spectral resolution of readily available scintillators and proportaional counters (PCs) available at the time, began investigating the possibility of using a variety of semiconductor materials in their place. A number of candidate materials are mentioned in the literature of the time including High Purity Germanium (HPGe), CdTe and HgI.2 . In spite of its superior energy resolution it was widely recognized that the added complexity levied by the cooling requirements of germanium detectors were a significant drawback to their use. Consequently, individual groups began investigating the feasibility of CdTe deployment in a space environment as early as 1976 [98] and eventually fielded a small number of CdTe-based spectrometers. The first such deployment, that I am aware of, was carried out as part of the International Sun-Earth Explorer (ISEE) program. The ISEE series of satellites was conceived as a close international partnership between the National Aeronautics and Space Administration (NASA) and European Space Agency (ESA). This consisted of a total of 3 separate spacecraft that were launched beginning with ISEE-1 and -2 on 22 October 1977 ending with the launch of ISEE-3 less than a year later on 12 August 1978. For this mission ESA was responsible for ISEE-2 and NASA for ISEE-1 and -3. The primary objective for this partnership was the study of space weather and, in particular, the character and conditions of Earth’s magnetosphere. For this reason ISEE-1 and -2 were placed in a highly elliptical orbit around the Earth with an apogee extending to 23 Earth radii (R⊕ ), while ISEE-3 was placed outside of the Earth’s magnetosphere at the L1 Lagrange point between the Earth and the Sun [108]. In this way ISEE-1 and -2 would monitor the environment around the Earth while ISEE-3 would provide a data point in a region outside the influence of the Earth’s magnetosphere. The planning phases of the ISEE program had started prior to the announcement of the existence of GRBs to the public in 1973, however, NASA had adopted a policy endorsing the modification of instruments under construction in order to accommodate studies to advance GRB science. As a result the ISEE-1 and -3 missions were modified to accommodate the addition of GRB monitors. For ISEE-

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Fig. 1 Schematic cross section of the 3.rd CdTe spectrometer system flown in space (reproduced with permissions from [74]). Each spectrometer contained 2 rectangular CdTe detectors measuring 22 .× 7 mm with a thickness of 2 mm (shown here on the 7 .× 2 mm cross section). The P78-1 satellite included 4 of these spectrometers in total

1 this instrument suite included a CsI scintillator system supplied by Max Planck Institut (MPI) and a 6 cm.2 array of CdTe detectors with unspecified thickness supplied by Goddard Space Flight Center (GSFC) [31, 71]. To my knowledge, the CdTe detectors launched with ISEE-1 represent the first spaceflight use of such detectors. The ISEE-3 spacecraft was also equipped with a passively cooled (to approx. 90 K) HPGe spectrometer which represents the first spaceflight use of that material as well [108]. The very first germanium detectors to have flown in space were, however, launched with the satellite 1972-076B into a polar orbit [73], also for the characterization of GRBs. Slightly after the ISEE array was deployed the P78-1 “Solwind” satellite was launched on 24 February 1979 carrying with it an additional CdTe array aloft [74]. In contrast to the ISEE instrument, for which details are hard to come by in the literature, the array for this instrument is reasonably well documented. Here the Gamma Ray Environment Sensor (GEMS) instrument consisted of 8 separate 2 mm thick rectangular CdTe detectors measuring 7 .× 22 mm (2 per GEMS module) and were surrounded by an active CsI shield (see Fig. 1)1 . The primary purpose of this instrument was for the measurement of bremsstrahlung X-rays emitted from the Earth’s atmosphere. This mission survived until it was decommissioned and ultimately became the target of a U.S. ASM-135 anti-satellite weapon (ASAT) test conducted on 13 September 1985 that terminated its existence.

1I

speculate that 4 of these CdTe detectors, totalling 6.12 cm.2 , very likely made up the CdTe array in the ISEE-1 payload, however, I unfortunately cannot confirm this at present.

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1.4 General Progress in X-Ray Astronomy and New Imaging Techniques (1970–1990) The rocket flights of the 1960s gradually expanded the number of known astrophysical X/.γ -Ray sources leaving many questions as to their origin and even their full distribution on the sky unanswered. This changed with launch of Uhuru (Sect. 1.2) which provided the first all-sky survey of X-ray sources in the 2– 20 keV band. However, the Uhuru instrument consisted of a pair of collimated proportional counters: one with a 0.5.◦ .× 5.0.◦ FoV and the other with a square 5.◦ FoV (FWHM) [77]. In spite of its limitations, Uhuru identified a wide variety of X-ray sources and phenomena including varieties with significant temporal variability. Further study to reveal their nature was required and fueled the demand for instruments with improved sensitivity, energy and angular resolution. To answer this call NASA placed a slew of instruments dedicated to the study of high-energy phenomna into LEO and beyond (e.g. SAS and OSO series) throughout the 1970s, including a series dedicated entirely to the study of X/.γ -ray astronomy. The first of the High Energy Astrophysical Observatory (HEAO) series, HEAO-A (or -1), conducted observations between 12 August 1977 and 9 January 1979, and HEAO-B (or -2) which launched on 12 November 1978 remaining in operation until 12 April 1981. HEAO-A hosted a number of instruments utilizing collimators to probe the higher energy sky in a similar respect to that achieved with Uhuru but with higher sensitivity [48]. At this point, the launch of X-ray astronomy payloads into LEO also started to become a much more international enterprise, with important contributions from the UK’s Ariel 5 mission [133], Japan’s Hakucho (a.k.a. Cosmic Radiation Satellite (CORSA-b)) [105], and Netherlands’ Astronomical Netherlands Satellite (ANS) [21, 39] to name a few.

1.5 Focusing X-Ray Imaging Telescopes The greatest technical leap of the decade, arguably, was demonstrated in the HEAOB [55] satellite. Renamed the “Einstein” observatory subsequent to its launch, Einstein introduced the first use of grazing incidence optics in conjunction with a position sensitive X-ray detector system for astronomy from LEO.2 This gave astronomers a focusing X-ray imager with high angular resolution (2. for the High Resolution Imager (HRI)) accompanied by a background reduction enabling many orders magnitude improvement in sensitivity over previous missions but with a narrow 25. Field of View (FoV) (HRI). This was the result of nearly 20 years of development from the formulation of the initial concept in 1960 [54] followed by a

2 Although

the ANS carried with it the first telescope equipped with grazing incidence optics injected into LEO [39] it was incapable of imaging by design.

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demonstration on a sub-orbital payload which captured the first soft X-ray images of the sun using this technique in 1965 [57], culminating in the launch Einstein’s launch in 1978 (for more detail Riccardo Giacconi’s Nobel lecture is an excellent entry point from a technical and scientific perspective [53]). These new capabilities enabled the Einstein observatory to produce many breakthroughs in the study of extended sources, such as supernova remnants (SNRs), as well as a wide variety of point sources and served as the forerunner of many of the X-ray observatories to come. This includes ROSAT [143] (1 June 1990– 12 February 1999), which would perform the first high resolution (7. ) all-sky survey using a focusing optic by systematically scanning the entire sky [149, 150]; the Advanced Satellite for Cosmology and AStrophysics (ASCA) mission [139] (20 February 1993–14 July 2000), which flew the first X-ray sensitive charge coupled device (CCD) focal plane used with a focusing X-ray optic at the heart of its Solid State Imaging Spectrometer (SIS) instrument [26] for astrophysics; as well as today’s premier soft X-ray observatories: the Chandra X-ray Observatory (CXO) (formerly the Advanced X-ray Astrophysics Facility (AXAF)) and XMM-Newton deployed just under 10 years later and which are both still in operation today. Unfortunately, the mirror technologies of the day only enabled imaging at energies up to approximately 10–15 keV, leaving those wishing to observe or monitor the sky at higher energies with limited options. This state of affairs would dramatically turn with the millennium expanding their reach up to energies approaching 100 keV; discussed later in Sect. 4.

1.6 Coded-Aperture Imagers Simultaneously astronomers and instrumentalists had begun to look into other methods to improve capabilities at energies above approximately 15 keV and struck upon a modification of the pinhole camera concept. Clearly, the use of a single pinhole together with a large position sensitive detector would not reach the sensitivities required by the astrophysics community, however, it was recognized that adding holes to increase X-ray throughput to a large, underlying detector plane coupled with the application of cross-correlation/FFT image reconstruction would enable the deployment of more sensitive wide-field, hard X-ray telescopes. In most applications an X-ray opaque “mask” is constructed so that a number of regions are left open to the sky some distance above the detector plane. In the presence of an X-ray source at celestial distances photons will register on a position sensitive detector plane and reproduce the mask pattern as .Nγ → ∞. Based on this principle it was realized that the positions of X-ray sources may be reconstructed through cross-correlation of detector plane images with the known mask pattern. After its proposal the coded-aperture imaging technique, originally termed a “Dicke camera” after its original proposer [40], was rapidly adopted by the community to fulfill

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this important roll. By the mid- to late-1980s coded-aperture imaging was widely recognized as a powerful technique for the wide-field monitoring of the X-ray sky in spite of relatively high backgrounds and source-contamination issues that are inherent to its use. Following the initial proposal in 1969 the first payloads making use of codedaperture imaging began appearing in launch manifests starting around the mid1970s. Initially the UK’s Ariel 5 mission deployed the first “pinhole” camera provided by NASA-GSFC using position sensitive proportional counters (PSPCs) and a 1 cm.2 aperture to conduct all-aky X-ray source monitoring and to search for transient events [133]. Subsequently, the first true 2D coded-mask wide-field imager, SL 1501, was tested on board a sub-orbital rocket payload in 1976 and successfully observed the galactic center resolving individual X-ray sources [62, 117]. By the early 1980s Japan’s Tenma mission (20 February 1983–22 November 1985) also had been equipped with a 1-D “Hadamard” mask as part of a 2 instrument Transient Source Monitor (TSM) with a wide 40.◦ .× 40.◦ FoV designed to detect and pinpoint the location of any potential GRBs and other transient events, etc. [138]. This was followed by the first LEO deployment of a 2D coded-aperture mask on the space shuttle mounted Skylab2 payload: Spacelab 2 X-ray Telescope (SL2-XRT) [153] with a 1024 cm.2 PSPC located 3 m below the mask. The SL2-XRT had a 6.◦ FoV and performed a 2.5–25 keV survey of the galactic center, extending observations that had been carried out by the Einstein observatory to higher energies, albeit at lower angular resolution, providing additional information on this region in a powerful demonstration of this technique [129]. Not long afterward on 1 December 1989, the Soviet-French GRANAT mission carried two large coded aperture imagers aloft: (1) the Sigma telescope [113] with a 794 cm.2 NaI detector plane configured as an Anger camera with a 2D tungsten mask mounted 2.5 m above the detector plane sensitive between 35 keV and 1.3 MeV with an angular resolution of 13. ; (2) The ART-P telescope, which consisted of 4 separate modules each containing a large 630 cm.2 active area PSPC capable of operation over the 4–60 keV energy range and a coded-aperture mask mounted 1.32 m above the detector plane, enabling a 6. angular resolution. The success of these missions paved the way for the introduction of future wide-field and hard X-ray imagers in astrophysics satellite payloads sensitive at energies above about 15 keV where, as mentioned earlier, grazing-incidence optics lose reflectivity and typically are only able to achieve a FoV at about the 1.◦ .× 1.◦ scale maximally. Following the development and astounding performance of grazing incidence optics and the introduction of coded aperture imaging between the late 1970s and the mid 1990s orders of magnitude improvements in sensitivity were achieved primarily using only proportional counters and scintillators. Beginning in the 1990s additional improvements in semiconductor manufacturing led to the adoption of CCDs and accelerated activity in the development of CdTe as well as the development of CZT would lead to, what I consider, the CdTe/CZT revolution in astrophysics, discussed later in Sect. 3.

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Dawn of the Solid State Imagers

By the early- to mid-1990s grazing-incidence telescopes (Sect. 1.5) and codedaperture imagers (Sect. 1.6) were firmly established as complementary techniques: the former enabling high-resolution (arcsec) observations soft X-ray sources and the X-ray sky and the latter providing a monitoring and survey capability for large swaths of the sky with moderate (arcmin) angular resolutions at all energies. While both techniques are reliant on position sensitive detector planes, all of the instruments of the day made use of either position sensitive proportional counters or Microchannel Plates (MCPs) or some form of segmented scintillator system or Anger camera, etc. During this time development of Si-based CCD had been progressing and gradually reaching a level of maturity acceptable for spaceflight [25, 47]. As concepts for the next-generation of high-energy wide-field monitors and focusing telescopes took on their final forms throughout the 1990s a rapid shift toward position sensitive detectors based on semiconductor materials of all types began to occur. At this point lithium-drifted Ge and High Purity Germanium were considerable frontrunners in addition to Si and all had been flown in various missions since the 1970. The significant difficulties associated with the cooling of these detector systems kept some focus on the development of room-temperature semiconductors over this period albeit at a relatively low level. By the end of the 1980s HgI.2 was considered the forerunner room temperature material and had been included on at least two balloon payloads by the end of 1982 [121, 147] enabling astrophysical observations of the black hole binary Cyg-X1 in conjunction with the Japanese Hakucho mission in 1980 [107]. However, outside of astronomy improvements in CdTe growth and fabrication were enabling some commercial applications (e.g. [43]). Eventually improvements in CdTe growth techniques and the development of CZT would make possible the production of detectors in the volumes and quality required for next generation astrophysics experiments turning the tables in dramatic fashion.

2 Early Semiconductor Detector Developments and the Deployment of the First Imagers The 1970s and 1980s saw some initial experimentation and deployment of useful semiconductor detectors for use in space science, of particular interest here CdTe and Ge detectors (Sect. 1.3). These were simple spectrometers mounted into collimators with no intrinsic imaging or position sensing capability of their own. In the early 1990s long-term development of semiconductor imaging technologies that has begun in the mid-1970s for heliophysics, astrophysics, and planetary science began to be deployed. This was initiated by the recognition of the potential

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improvements that semiconductor detectors, of all compositions, could enable leading to rapid development in this arena, initially for Si-based CCDs.

2.1 Early Space Science CCD Development One of the earliest deployments of CCDs for space science occurred with the launch of the Giotto Halley Multicolour Camera (Giotto-HMC) using a Texas Instruments (TI) virtual phase CCD (VPCCD) on 14 May 1986. As the instrument name strongly implies, the purpose of the mission was to intercept and conduct in situ observations of Halley’s comet [84, 85] during its close flyby of the Earth in 1986. This line of CCDs was an outgrowth of a JPL/TI led development program [94] conducted for the Galileo probe which performed a fly by of Venus before settling into orbit around Jupiter 7 December 1995 after its launch 6 years earlier on 18 October 1989. In the case of the Galileo mission, Si-based CCDs were quickly recognized as a key technology for the improvement in imaging sensitivity that would be critical for observation of the Jovian system, particularly during close fly-bys of the Jovian moons. A joint effort between Jet Propulsion Laboratory (JPL) and TI was initiated in the mid-1970s to replace the SeS.2 vidicon based imaging system used in the Mariner and Voyager probes that served as the backbone of planetary imaging (cf. Voyager imaging science subsystem (Voyager-ISS) [134]) with a new detector plane. After a 15 year development effort the Galileo solid state imager (Galileo-SSI) was deployed in a system very similar to that of the Voyager-ISS excepting the use of a 800 .× 800 pixel (15.2 .μm) VPCCD [17, 78]. This program was also intimately connected to the development of the HST Wide Field/Planetary Camera (WF/PC) [152] as well. The WF/PC was equipped with a 4 .× 4 array of these CCDs [152] and launched shortly after Galileo on 24 April 1990. Finally, a slightly different version of these VPCCDs were launched with the Japanese Solar-A Mission renamed Yohkoh (translation: Sunbeam) a little over a year later on 30 August 1991. One difference between the CCD flown with Yohkoh and that of the Galileo and HST instruments is that it was expanded to support a 1024 .× 1024 array of slightly larger square pixels (18.3 .μm). The primary difference, however, is that this CCD was built for the high-resolution observations of the sun in soft X-rays. It was flown at the focal point of a grazing incidence optic [87, 144] making it one of the first of a new-generation of CCD based X-ray telescopes including ASCA [26, 139], which was a Japanese astrophysics mission with significant US participation, and finally the Chandra X-ray Observatory (CXO) and X-Ray Multi-Mirror Mission Newton (XMM-Newton) at near the turn of the millennium, briefly discussed earlier in Sect. 1.5.

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2.2 Non-Silicon Semiconductor Imager Development Just after the first generation of Si-based CCD detectors were deployed the development, construction and testing of imaging detectors using Ge, CdTe and CZT began to occur. The first exemplar of a non-Si semiconductor imaging instrument (occasionally identified as the “Birmingham experiment”) that was successfully tested in a near-space environment, consisted of a 9 element HPGe configured in a 3 .× 3 array of detectors with a 0.2 mm gap between adjacent crystals. Each individual crystal measured 15 .× 15 mm with a 50 mm thickness along the observation axis [131, 132]. A rectangular coded aperture mask was placed 980 mm above the upper surface of the detector plane and the payload launched together with the Gamma-Ray Imaging Spectrometer (GRIS) [145]. The GRIS payload also was made up of an array of HPGe detectors, deployed for the same purpose and was, notably, part of a NASA initiative launched in 1982 for the creation of .γ -ray detectors with improved sensitivity for future spaceflight opportunities. During a September 1993 flight, the Birmingham instrument successfully imaged the CygX1 and obtained both images and measured the spectrum of the Crab nebula, a standard candle in X-ray astronomy, demonstrating the feasibility of coded-aperture imaging using semiconductor detectors for spaceflight. This was seen as a potential forerunner to the next-generation of wide-field instruments under development at that time while recognizing, as before, the difficulties associated with maintaining low temperatures over the large detector areas required, 1000s of cm.2 . Accordingly, development efforts for the spaceflight use of room temperature semiconductors began to gain momentum at about the same time that the need for these large detector planes became clear. A few years after the first viable CZT detectors became available the first spaceflight CZT detector demonstration was carried out as part of the Piggyback Room Temperature Instrument for Astronomy (PoRTIA) payload in 1995 along with a HgI.2 detector in an effort led by GSFC [111, 112]. Though the PoRTIA instrument only carried a single 6.5 .× 6.5 cm, 1.9 mm thick CZT crystal, this successful flight represents a significant milestone leading to the production of large-scale CZT detector planes. Additional, parallel efforts, were also underway for the development of position sensitive detectors using an anode segmented into strips, e.g. strip detectors with pitches as fine as 100 .μm [111, 112] at GSFC. Beyond GSFC a number of other groups were pursuing the development of strip detectors and simultaneously were pursuing balloon flights to demonstrate their own technologies (e.g. University of New Hampshire (UNH) [125], University of California, San Diego (UCSD) in collaboration with Aurora technologies [41, 42]). Although the CZT crystals acquired at the time were by no-means defect free the quality and volume was sufficient to stimulate interest and propel further development. The primary problem for many of the groups aiming to produce finely pixelated detector planes shifted to development of the front-end readout system and the search and/or development of

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application specific integrated circuits (ASICs) that could be safely deployed into the space environment.

2.3 Further Advances in Astrophysics At the same time as these developments were well underway and the Compton Gamma-Ray Observatory (CGRO) (5 April 1991–4 June 2000) along with the Burst and Transient Source Experiment (BATSE) instrument were placed into orbit and began observations. The detector system consisted of 8 separate modules, each containing 2 detectors: (1) the Large Area Detector (LAD), NaI(Tl) scintillators with a 1.27 cm thickness and 2025 cm.2 area, sensitive in the energy range between 30 keV and 1.9 MeV; and (2) the Spectroscopic Detector (SD), also composed of NaI(Tl) but with a 127 cm.2 area and 7.62 cm thickness optimized for spectral response. Each of these modules were placed at the corners of the CGRO in order to provide some source localization capability while enabling observation of the full visible sky [45, 110]. During the course of its operations BATSE detected approximately 1 GRB every day. The localization capability of BATSE enabled astronomers to determine that the distribution of GRBs was definitively isotropic strongly implying an extra-galactic origin but the mechanism and source could not yet be identified, see [44] for a classic review of the status of the investigation into GRBs circa 1995. In the bottom half of that decade the Satellite italiano per Astronomia X (BeppoSAX) (30 April 1996–30 April 2002) mission was fast approaching its launch date. BeppoSAX was a major ASI mission with significant participation of the Netherlands Agency for Aerospace Programs (NAAP), or in Dutch, Nederlands Instituut voor Vliegtuigontwikkeling en Ruimtevaart (NIVR) [22]. The payload was designed to observe the X-ray sky over a wide 0.1–300 keV energy band for the detection and characterization of variable X-ray sources; GRBs were of particular interest but other variable sources that permeate the galactic and extra-galactic Xray sky were also of critical interest. The key innovation of BeppoSAX mission was the inclusion of both wide- and narrow-field X-ray instruments for the express purpose of performing rapid follow-up observations of transient sources detected in the wide-field instrument with the narrow-field instruments for the acquisition of higher-resolution source positions and spectra. More specifically, it was outfitted with two Wide-Field Cameras (WFCs) [22] oriented in opposite directions. Each of the identical WFCs consisted of a PSPC coupled to a coded aperture mask placed 700 mm above the surface of the detector plane. This combination resulted in an instrument with a 20.◦ .× 20.◦ FoV and a 5. angular resolution sensitive over the 1.8–28 keV energy band. Further, BeppoSAX was equipped with four grazingincidence narrow field instruments with the objective of performing X-ray followup observations within about 1/2 day in the soft (0.1–10 keV) X-ray band. BeppoSAX was able to precisely localize GRB to arcmin resolution and successfully performed the first follow-up observations of GRBs [37].

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Fig. 2 The .T90 distribution, i.e. the distribution of the width of the time window within which 90% of the total events for a single GRB are detected, from the BATSE-4B catalog. The bimodal distribution implied the existence of two different .γ -ray emission mechanisms but, for events lasting less that 1 s, followup with BeppoSAX was not possible due to the constraints of the mission

Critically, these high-angular resolution positions enabled followup observations from the ground, identification of host-galaxies, and a measurement of their redshift (cosmological distance) for the first time [114]. These observations placed the origin of the long-GRB population firmly within distant galaxies, confirming the primary conclusions drawn from the BATSE data but left some questions as to the origin of short-GRBs which, due to their prompt emission lasting less than 1 s (see Fig. 2), were undetectable by the time a follow-up observation could be conducted (see [114] for a good review after the discoveries enabled by BeppoSAX). At the turn of the millennium the success of the BeppoSAX mission demonstrated the value of followup observations and made significant contributions to our understanding of GRBs but left many questions as to their origin and nature unanswered due to the limited effective area of the detector system itself and the limitations of its followup strategy. Even prior to the launch of BeppoSAX, proposals for much larger observatories with effective area of an order of magnitude larger had been in circulation. The results gathered up to that point underscored the need for this class of new, larger, instruments with greatly improved reporting and follow-up capabilities. Here the “new” materials CdTe and CZT would play a key role in their realization.

3 The CdTe/CZT Revolution At the close of the last millennium the first true imaging detector utilizing segmented semiconductors had been successfully demonstrated on high-altitude balloon flights boosting confidence that the coded-aperture technique could be successfully deployed in the space environment. Additionally, the recent success of the BeppoSAX mission had also demonstrated the feasibility and importance of followup observations utilizing instrumentation within the same spacecraft and Mission Operation Center (MOC) to provide actionable alerts for rapid observations from other observatories at multiple wavelengths. With BeppoSAX serving as a

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rapid alert system, the collective use of the assets of the astronomical community enabled a revolution in our understanding of one of the most enigmatic transient phenomena GRBs. Building on technologies demonstrated in the mid-90s, which produced some of the first non-Si semiconductor based imaging instruments (cf. Sect. 2.2), segmented detectors with one CdTe or CZT crystal serving as a discrete pixel were scaled up dramatically enabling the first generation of large area, wide-field monitors. This was made possible, in large part, due to the increasing availability and quality of commercially produced material which allowed astronomers to overcome the intrinsic limitations in effective area imposed by the use of gas-filled position sensitive proportional counters at high energy, and avoid the complexity of integrating a largescale cooling unit into this generation of all-sky monitors. Two missions containing this next-generation monitoring technology were proposed and fielded in the early 2000s to survey the hard X-ray sky and fulfill the rapid-alert role of the BeppoSAX mission: INTEGRAL (Sect. 3.1) and Swift (Sect. 3.2).

3.1 Integral The International Gamma-Ray Astrophysics Laboratory (INTEGRAL) was designed and deployed to provide high-resolution spectroscopy as well as precise positions of X/.γ -ray sources over the 15 keV to 10 MeV energy range. It was conceived as a ESA/NASA/Russian collaboration whose baseline design contained two primary instruments, as well as two secondary monitors, just prior to its selection as a medium-class mission within the ESA “Horizons 2000” framework in 1993 [130]: 1. A spectrometer consisting of 3 .× 3 array of “large volume” 68 mm diameter, 80 mm long Ge detectors sensitive between 15 keV and 10 MeV. For background reduction these detectors were to be surrounded by an active BGO shield. Together with a coded-aperture mask fixed 4 m away from the surface of the detectors, an angular resolution of 1.4.◦ was expected with a 10.◦ FoV Full-Width Half-Maximum (FWHM) and a detector area of 327 cm.2 . 2. A wide field coded-aperture imager utilizing 3 stacked CsI detector planes coupled with a BGO active shield mounted between the lower CsI plane and the spacecraft surface for background reduction. As originally envisioned, each CsI detector plane would have contained 2500 individual 1 cm.2 bars each individually coupled to a Si PIN diode; a 2500 cm.2 active area in total. With a coded-aperture mask mounted at a distance of 4 m above the detector plane an angular resolution of 17. would have been possible over a 70 keV to 10 MeV energy range (contingent on the mask transparency at the higher energy range). By 1995 the wide-field coded-aperture imager had been renamed Imager on Board the INTEGRAL Satellite (IBIS) and the upper CsI detector plane replaced with the ISGRI instrument, a 2600 cm.2 CdTe detector plane consisting of 2 mm

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Fig. 3 (Left) the ISGRI “Polycell” (from [90]) and (Right) the BAT “Detector Module” (from [16]). The ISGRI polycell supports the operation of a 4 .× 4 array of 4 mm square, 2 mm thick CdTe crystal read out by 4 ASICs, each with 4 input channels. The BAT-DM, on the other hand, supports the readout of a 8 .× 16 array of CZT crystals of the same size and thickness

thick, 4 mm square detector elements produced by AEROTECH (now ACRORAD). The two lower CsI detector planes, now designated Pixelated Imaging CsI Telescope (PICsIT), were reduced to a single 3100 cm.2 plane. Ultimately the form of this detector plane underwent little change from this point until its launch from the Baikonur, Kazakhstan on 17 October 2002 and is currently still in operation. Of note, the mission occupies a highly elliptical 9000 km.× 154,000 km (approximately 1.4 R⊕ .× 24 R⊕ ) orbit which coincidentally happens to be quite similar to that of the ISEE-1 mission’s orbit that carried the first CdTe detectors into space (see Sect. 1.3). The ISGRI instrument was composed of 16384 individual CdTe elements selected from pool of 29600 CdTe crystals. The full detector plane design was modularized to facilitate efficient and safe integration where the fundamental building block consists of a single “polycell” containing a 4 .× 4 array CdTe crystals situated on the upper surface (see Fig. 3). On the back a 2 .× 2 array ASICs is mounted each of which support 4 readout channels, 16 total. A 8 .× 16 array of “polycells” are then combined into a single Modular Detection Unit (MDU) and, finally, a 2 .× 4 array of MDUs comprise the whole of the ISGRI detector plane. At the time of its launch the ISGRI array was, by far, the largest CdTe detector ever placed into space.

3.2 Swift At the same time, efforts within NASA were concentrated on the development and launch of the Swift mission whose primary goal would be the rapid identification and follow-up observation of GRBs within 60 seconds or less. Where followup observations with BeppoSAX required up to a 12 hour wait following the detection

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Fig. 4 The layout of the Swift mission (modified from [51]). The Swift-BAT coded aperture telescope is made up of 256 DMs (see Fig. 3) each containing 128 individual CZT that all together make up the 32768 pixels of the BAT detector plane

of an event, Swift was designed to automatically detect and localize X-ray transients with a single wide-field monitor then slew the spacecraft to place a GRB, or other transient X-ray source, within the FoVs of the narrow field instruments capable of conducting more detailed observations and precise (arcsec scale) localization, all without human intervention. The Swift Mission was selected for a Phase A study in January 1999 and then for flight in October of the same year under the NASA Explorer’s program as a medium class mission MIDEX [51] with the primary objective of uncovering the source and nature of the environment about GRBs. To achieve this Swift was equipped with the following 3 instruments: 1. a wide field instrument, the Swift BAT [16], which would be responsible for the initial detection of GRBs and their automated localization (see Fig. 4). 2. a soft grazing incidence X-ray telescope, the Swift X-Ray Telescope (XRT), which would provide follow-up observations and provide high-quality spectra and refined positions for the GRB afterglow. 3. a UV telescope, the Swift Ultraviolet/Optical Telescope (UVOT), which was added for yet better refinement and characterization of detected GRBs in the EUV. Similar to the ISGRI instrument the Swift BAT was composed of discrete detector elements bonded to ASICs and assembled into tileable modules (see Fig. 3) which were assembled into a very large detector plane [16], but with some important key differences. First, the BAT instrument made use of 4 mm.× 4 mm, 2 mm thick CZT procured from eV products in place of CdTe. Second, the Swift-BAT detector is about a factor of 2 larger than the ISGRI detector plane and contains a 32768 individual detectors with a total active area of approximately 5242 cm.2 active area with an extent of 1.2 m .× 6.0 m. Finally, the FoV of the BAT instrument is

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much larger than that of ISGRI subtending roughly 1.2 sr Full-Width Half-Intensity (FWHI) maximizing the number of bursts that may be imaged and pursued. Critically, the Swift mission also was built with the ability to rapidly downlink derived transient event information through the Tracking and Delay Relay Satellite (TDRS) system for rapid distribution to ground-based observers. In this way Swift was designed to enable the determination of the redshifts, a proxy for cosmological distances, for as many GRBs as possible. Over 19 years of nearly continuous operation since its launch on 20 November 2004, the Swift mission has succeeded magnificently in this goal and remains the premiere GRB and X-ray transient monitor in operation to date also remains the largest CZT array ever launched.

3.3 The Dawn GRaND Experiment It is important to note here that, although the Swift BAT is the first imager and instrument to make use of CZT in a major astrophysics mission, the first CZT utilized in spaceflight was actually deployed on the planetary science mission Dawn. At the same time that INTEGRAL ISGRI and the Swift BAT were in development, the planetary science community had also been conducting their own investigation into the use of CZT for the characterization of the elemental compositions of planets and asteroid through nuclear line-emission spectroscopy [116]. Using this information, together with in situ observations from other instruments, information regarding the formation history of small bodies may be deduced. For this purpose Dawn carried 3 instruments including the Framing Camera (FC), a Visible and Infrared Spectrometer (VIR), and GRaND (see Fig. 5). Of

Fig. 5 (Left) A cross section of the GRaND instrument that was mounted to the deck of the Dawn mission (reproduced from [115] with permissions)

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primary interest here is GRaND which consisted of: (1) a bismuth germanate (BGO) scintillator with 300 cm.2 volume at its core; (2) a 4 .× 4 array of CZT 10 mm.× 10 mm.× 7 mm crystals, each configured as co-planar grids (CPGs) and optimized for spectroscopic measurements; (3) a two L-shaped boron loaded plastic (BLP) scintillators surrounding the sides of the BGO and CZT array primarily to provide sensitivity to neutrons; and (4) a two BLP phoswitch detectors located above and below the CZT and BGO instruments which are also sensitive to neutron interactions [115]. The Dawn mission was launched on 27 September 2007 and entered orbit around 4 Vesta on 16 July 2011 within the asteroid belt after a nearly 4 year cruise. Following a 14 month observation period Dawn began its departure from 4 Vesta orbit on 25 July 2012 beginning a 2 year transit to 1 Ceres arriving on 6 March 2015. Dawn collected data for another 2 years around 1 Ceres before end of mission on 11 November 2018. Dawn, though inactive, remains in orbit around 1 Ceres and carries with it the most well traveled CZT array fielded thus far.

4 Beyond Wide-Field Imagers: CZT Comes into Focus Up to the early- to mid-2000s all CdTe or CZT instruments deployed were either simple spectrometers or used as a detector plane in a coded-aperture telescope, or other wide-field imager, but not any sort of focusing optic. This is due in large part to the limitations of grazing incidence optics whose reflectivity rapidly decreases beyond energies around 15 keV. These mirrors are typically coupled with CCD’s such as those found in the Swift-XRT [28], Chandra or XMM Newton given their availability and the overlap in usable energy ranges. Advances in X-ray mirror technologies during the late 1999s/early 2000s significantly extended the effective energy range of grazing incidence mirrors. The introduction of “super-mirrors”, e.g. [154], with adequate response up to approximately 100 keV made possible the potential deployment of hard X-ray missions with arcsec angular resolutions for the first time. Since Si detectors become nearly transparent to hard X-rays pixelated CZT detectors, which had reached a sufficient level of maturity in the preceding decade, were chosen as a natural alternative. The primary drawback of these optics was, and remains, the long focal lengths required to realize imaging up to 80 keV. Nonetheless initial balloon flights to prove out these concepts were conducted by at least three groups during the early 2000s in preparation for a potential space mission: High Energy Focusing Telescope (HEFT) [63], International Focusing Optics Collaboration for μ-Crab Sensitivity (InFOCμS) [106], and High Energy Replicated Optics (HERO) [118, 119]. Ultimately the HEFT group expanded on the mirror and detector technologies demonstrated in their balloon flights and proposed the Nuclear Spectroscopic Telescope Array (NuSTAR) mission as a Small Mission Explorer (SMEX) to

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Fig. 6 (Top) The NuSTAR telescope with the optics fully deployed; the instrument as a focal length of 10.4 m. (Bottom) Major components of the NuSTAR instrument in it’s launch configuration before extension of the mast (from [64])

NASA [64]. NuSTAR was launched on 13 June 2012 and made use of a deployable boom (see Fig. 6) to realize the focal lengths necessary to produce the world’s first and only, spaceflight, focusing hard X-ray telescope. Technologies that had been developed by AEC-Able Engineering, now part of ATK space systems, in the previous decade for the Shuttle Radar Topography Mission (SRTM) experiment demonstrating the space use of 50 m extensible and retractable masts from the Space Shuttle [81]; and advances in CZT detector technology were brought together by the NuSTAR collaboration to produce the world’s first and, currently, only operating space-based focusing hard X-ray telescope. NuSTAR has provided unprecedented sensitivity in the moderately hard X-ray regime between 15 and 85 keV enabling improved estimates of the spins and masses for select black holes (e.g. [140]), precise morphological studies of the distribution of residual radioactive isotopes in Cassiopeia A, a supernova remnant, that have been gradually decaying since the original supernova explosion [59], resolution of up to 33%-39% of sources making up the hard component of the cosmic X-ray background (CXB) confirming the existence of an obscured population of Active Galactic Nucleis (AGNs) [65], as well as a series of solar observations [60], etc. It can be expected that the next generation of mirrors and CZT and/or CdTe detectors will play a significant role in this energy range in the years ahead in all branches of space science.

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5 Pixelated and Strip Detectors Become Standard The amazing successes of the ISGRI (Sect. 3.1), BAT (Sect. 3.2) and NuSTAR (Sect. 4) instruments have heightened the profile and familiarity of CZT and CdTe within the astrophysics community where it is now viewed as a fairly standard material, although the construction and deployment of such detectors remains a significant challenge. The complexity of the assembly process for the ISGRI and BAT instruments, which both used discrete crystals as single detector pixels is widely recognized, as are the limitations in the minimum achievable pixel size and the difficulties associated reduction of parasitic noise sources on the interconnects of such arrays. This was avoided with the use of pixelated CZT in the NuSTAR instrument launched nearly a decade later. Since the mid-1990s (see Sect. 2.2) development of CZT, CdTe or other non-Si semiconductor for deployment in space generally includes detector crystals with some form of anode and/or cathode segmentation. The most common configurations are the use of an array of square anode pixels or the application strips on the anode and cathode side where the strips on opposite sides of the crystal are oriented orthogonally to one another, so-called Double-Sided Strip Detectors (DSSDs). The latest notable example is the HPGe based Compton Spectrometer and Imager (COSI) mission [142] a Compton telescope for astrophysics sensitive between 0.2–3 MeV which makes use of Double-Sided Strip Detectors and is currently scheduled for a launch in 2025 as NASA’s latest SMEX mission. For CZT, CdTe and other room temperature semiconductors spaceflight development within the U.S. and Europe has been primarily focused on the development of pixelated detectors since at least the early 2000s, with significant interest in CdTe DSSD development in Japan. The Indian Space Research Organization has also fielded a number of instruments for all branches of space science reliant on pixelated CZT detectors. A key component of this development, regardless of the segmentation strategy, has been improvement in detector contact deposition over the past 15 years as well as the production and availability of low-power ASICs. These advances have enabled the creation of high resolution position sensitive detector systems that may be supported within the power and thermal constraints of spaceflight; the specific constraints of each mission are naturally dependent upon the target spacecraft or platform (e.g. SmallSat, CubeSat, International Space Station (ISS), etc). Although the trend toward finer pixelization for many applications, coupled with the requirement for large areas in non-focusing instruments produce significant challenges in the design of viable instrumentation, corresponding reductions in device power density over the last 20 years have enabled the realization of finely pixelated (or fine pitch strip) detectors at the 100 .μm level and smaller (see Table 1) that may be credibly considered for spaceflight. This is enabling a new generation of highly capable instruments while avoiding many of the drawbacks and difficulties associated with the construction of the first

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Table 1 Characteristics of selected and potential spaceflight ASICs used with CdTe and/or CZT based detector systems P/N or name ISGRI95 [15, 23] XA1.2 [16] HEFT [30, 35]

N.Ch,In 4 128 1054

Pwr. [mW/ch] 2.8 2.8 −3 .47 × 10

Year Intro. 1996 2000 1998

NuASIC

1024

.47

× 10−3 to .92 × 10−3

2008

VATASGD [135, 136]

64

0.3

2003

IDeF-X [93]

64

0.6–2.8

2006

HEXITEC [80, 124]

6400

.220

× 10−3

2009

Notes ISGRI BAT [16], Mfg. Ideas HEFT Balloon Flight Direct Bond: 24 .× 44 498 .μm Pitch NuSTAR Precurssor NuSTAR [64] and ProtoEXIST2 [12] Direct Bond: 32 .× 32 604.8 .μm Pitch Note: Pwr. dep. on operation cond. Hitomi-SGD [136], Mfg. Ideas FOXSI-3 [50] Basis for Caliste-64, -256, and -SO STIX uses Caliste-SO [95] SVOM uses the IDeF-X ECLAIRs [52, 89] Note: At least 7-variants w/diff. Pwr. Direct Bond: 80 .× 80 250 .μm Pitch

generation of wide-field imagers and has lead a large fraction of the space-science community to adopt pixelated CZT detectors as a fairly ubiquitous standard, with a few notable exceptions (e.g. position sensitive virtual Frisch grid detectors [96], etc.).

6 Recent Development Activities and Missions Over the last 15 years the supply of ASIC, CZT and CdTe have improved dramatically enabling the development of many different instruments and missions cutting across all segments of space science. Below I outline some of the most recent activities within the last decade and highlight some of the ongoing efforts.

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6.1 Wide-Field Instrumentation for Astrophysics The recent discovery of gravitational waves and the detection of only a single electromagnetic counterpart, designated GW170817, has highlighted the need for improved wide-field monitoring with prompt detection, characterization, and reporting capabilities. There are currently a large number of missions and concepts under development utilizing Si, scintillator, CZT/CdTe, etc., often combined within a single mission. The High Resolution Energetic X-Ray Imager (HREXI) program (formerly ProtoEXIST) has developed a number of tileable CZT detector plane architectures that utilize large numbers of 2 cm.× 2 cm, 5 or 3 mm thick pixelated CZT detectors. Two prototypes have been qualified in successful high altitude balloon flights, ProtoEXIST1 (2009 flight) [11] utilizing an 8. × 8 array of detectors with a 2.5 mm pixel pitch and ProtoEXIST2 (2012 flight) [12, 70] which utilized the NuSTAR ASIC (NuASIC) to reduce the pixel pitch of the array to 604.8 .μm. The HREXI effort is ongoing with a refinement of the ProtoEXIST2 detector plane architecture underway based on lessons learned from the ProtoEXIST experience. Depending on the deployment method chosen, detector areas of up to approximately 4 m.2 are feasible on a large spacecraft. Currently low-cost implementations are under study on SmallSats to enable the launch of multiple independent spacecraft into LEO. If realized, this detector net would achieve all-sky coverage with high sensitivity over the 3 keV to 1 MeV (approx.) energy range and while enabling arcmin localization, rapid reporting and characterization of transient sources including Gravitational Wave (GW) counterparts. Meanwhile, the Indian Space Research Organization designed and deployed a mission to LEO that is, in many respects, similar to Swift: ASTROSAT [128] (28 September 2015-Present). Like Swift, ASTROSAT is equipped with a widefield monitor, CZT Imager (CZTI), which is a coded aperture imager based on 4 cm.× 4 cm, 5 mm thick General Electric (GE) (formerly Orbotech, formerly Imarad) CZT with a total active area of 976 cm.2 and a coded-mask affixed 481 mm above the detector plane [18, 29]. In the first 16 months of operation CZTI was able to detect approximately 96 GRBs, performed timing measurements and simultaneously probed the hard X-ray polarization of the Crab nebula [120]. In the interim CZTI continues operation and regularly reports on the occurrence and properties of transient X-ray events including GRBs. On an additional note, the baseline detector plane architecture of the CZTI instrument has been used on at least 2 other spaceflight missions in which Indian Space Research Organization (ISRO) participated or led: Chandrayaan-1 (Sect. 6.6) which carried out observations of the moon from lunar orbit and CORONAS-PHOTON, a Russian payload where ISRO provided a hard X-ray instrument for solar observations (Sect. 6.7). To expand their wide-field transient monitoring capability, ISRO has proposed and is developing the Daksha [19, 20] high-energy transient mission with a heavy focus on rapid detection and characterization of GW counterparts. One of the instruments responsible for the localization of hard X-ray sources will utilize

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the same baseline CZT detector plane architecture which ISRO has fielded since the launch of Chandrayaan-1 but reconfigured and optimized to provide full sky coverage to maximize the detection probability of Gravitational Wave event counterparts. Another mission focused on the detection of GW counterparts is the joint sino-ESA effort, the Space-based Astronomical Variable Object Monitor (SVOM) mission, which is approaching its launch date, expected in 2023, and includes a suite of instrumentation to characterize X/.γ -ray transients including a CdTe based wide-field monitor ECLAIRs which makes use of the Imaging Detector Frontend (IDeF-X) ASIC. IDeF-X has been developed and flight qualified over approximately the last 15 years at the Commissariat à l’énergie atomique et aux énergies alternatives (CEA). The ECLAIRs detector plane utilizes an array of 6400 discrete 4 mm.× 4 mm, 1 mm thick CdTe crystals to produce an imaging detector with a total active area of 960 cm.2 in a manner analogous to that of ISGRI. With the placement of a 2D coded aperture mask 46 cm above the detector plane ECLAIRs will have a 22.1.◦ .× 22.1.◦ FoV [58] with a usable energy range extending from 4 keV up to 150 keV. SVOM will operate similarly to Swift in order to perform automated followup observation of transient sources for their characterization and dissemination of alerts to the community. On a final note, there currently are a large variety of wide-field instruments and mission concepts for their deployment in all phases of development targeting time domain multi-messenger astrophysics (TDAMM). These make use of a wide variety of detector systems which are not discussed here in any detail, and which are complementary and sometimes competitive with CZT and CdTe based instruments.

6.2 Hard X-Ray Focusing Missions The success of the NuSTAR mission unambiguously demonstrated the power of coupling new grazing incidence mirror technologies with CZT. Although this had been anticipated by a number of groups who were pursuing parallel development efforts (see Sect. 4) throughout the 2000s only one other such instrument has been deployed in a spaceflight mission. The Hard X-Ray Imager (HXI), was launched with the Hitomi mission (previously ASTRO-H or New exploration X-ray Telescope (NeXT)) on 17 February 2016 together with 3 additional instruments [136, 137]: (1) the Soft X-ray Imager (SXI) which built on heritage from the Suzaku (Astro-E) X-ray Imaging Spectrometer (XIS) [66] was a focusing X-ray telescope utilizing an X-ray CCD provided by MIT/LL; (2) the Soft X-ray Spectrometer (SXS) was the first micro-calorimeter used in spaceflight for astrophysics which conducted observations (e.g. [32]) and achieved an energy resolution of 5 eV; (3) the Soft Gamma-Ray Detector (SGD) [135] which was a low background Compton spectrometer optimized for the characterization of source spectra between 10 keV and 600 keV.

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The HXI shared many common features with NuSTAR including an extendable optical bench (i.e. mast) which would have enabled a 12 m focal length and would have been sensitive over the 5 to 80 keV energy range with a HalfPower Diameter (HPD) of 1. .7 (cf. NuSTAR approx. 1. ). The primary difference lies in the implementation of the detector system. Here the HXI made use of a combination of Si DSSDs and CdTe DSSDs. Ordered from the mirror toward the direction of the detector plane, the HXI consisted of a vertical stack of 4 layers of 0.5 mm thick Si detectors with a single 0.75 mm thick CdTe detector located at the bottom. The pitch of the strip pattern deposited on both Si and Cd detectors was 250 .μm. The stacking of detector planes mitigated the need to use a single, thick, detector crystal as was done in NuSTAR easing the fabrication requirements on the CdTe which, in contrast to CZT, remains difficult to grow into thick boules. Unfortunately, the Hitomi mission was lost on the 26 March 2016 shortly after the deployment of the optical bench for the HXI. However, during a short period between the 19 March and 26 March of that year HXI was able to conduct short observations of G21.5-09 (a supernova remnant) and the Crab nebula, the “standard candle” of X-ray astronomy [99].

6.3 Compton Imagers and Spectrometers Both the Hitomi HXI and SGD benefited from a long-running development program combining the use of Si and CdTe strip detectors, using CdTe from ACRORAD. In the case of the SGD this was used for the creation of sensitive hard X-ray spectrometer with polarization measurement capabilities [135]. This instrument has gone through multiple iterations of development over the last 20 years with one of the latest versions selected for inclusion and eventually launched with Hitomi. Like the HXI (see Sect. 6.2) the SGD was also able to conduct some observations beginning on 24 March 2016 prior to the loss of the mission two days later on 26 March 2016 [99, 136]. The SGD targeted a 10–600 keV energy range and was configured to function as a collimated instrument that would not required high positional resolution of individual events. The full instrument consisted of 3 detector units, each with their own collimator, and surrounded by a BGO active shield. Ordered from the collimator to the bottom of the instrument the 3 individual detector planes consisted 32 stacked 0.6 mm thick Si detectors followed by another 8 layer stack of CdTe detectors, each with a thickness of 0.75 mm. On the anode surface of both the Si and CdTe detectors, a square pixel pattern with a 3.2 mm pitch was applied over a 51.2 mm span, i.e. 16 .× 16 pixel pattern. With limitations in the size of CdTe crystals available each CdTe layer is actually consists of 4 buttable crystals in order to match the active area of the overlying Si detectors. The entire stack is surrounded by a 2 layer thick wall each consisting of identical 0.75 mm thick CdTe detectors [136]. In spite of its short lifetime this instrument managed to produce a measurement of the degree of polarization in the Crab nebula during the initial on-orbit checkout [69]

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and a new version of this, the mini-SGD, is scheduled to fly as part of a balloon payload from Alice Springs, Australia, this spring (2023) [100].

6.4 A Quick Note on XRISM: The Hitomi Successor Following the loss of the Hitomi mission Japan Aerospace Exploration Agency (JAXA) and NASA agreed to the fabrication and launch of a mission primarily to replace the loss of the micro-calorimeter, the SXS, which provides unique capabilities that have heretofore remained unrealized on orbit; the loss of the Hitomi mission is in fact the third failed attempt to deploy an X-ray micro-calorimeter to LEO. In light of the high-priority assigned to this instrument by JAXA, NASA and the high energy astrophysics community the X-Ray Imaging and Spectroscopy Mission (XRISM) mission was rapidly approved and is nearing launch expected sometime after August of this year (2023) [1]. In order to reduce mission risk and cost the decision was made to maintain the design of the Hitomi mission but remove the extensible optical bench, including the instruments mounted to it: the Soft Gamma-Ray Detector (SGD) (Sect. 6.3) and the Hard X-Ray Imager (HXI) (Sect. 6.2) [75, 141]. The SXS (renamed: Resolve) and the XIS (renamed: Xtend) largely retain the same capabilities as the instruments from the Hitomi mission but the two CdTe-based instruments, regrettably, must wait for another flight opportunity.

6.5 Instrumentation for Earth Observing Traditionally observation of the Earth in .γ -rays was originally carried out for nuclear weapons test ban monitoring (e.g. the Vela program briefly described in Sect. 1.2). In the 1990s the BATSE detection of a new and unexpected atmospheric phenomena [46], Terrestrial Gamma-Ray Flashs (TGFs), has fueled increasingly intensive research efforts over the past 30 years with over 1000 detections confirmed in a wide variety of high-energy instruments in LEO and is a problem that spans the study of Earth science, heliophysics and space-weather. An association between TGFs and thunderclouds was discovered almost immediately and confirmed in many subsequent observations. The current leading theories are that the intense electromagnetic fields generated in thunderclouds provide an acceleration mechanism for electron’s at high altitude up to GeV scale energies which can produce an upward directed Extensive Air Shower into space resulting in a flash of high energy photons that may be detected in our fleet of orbiting observatories. In order to study this phenomena the Atmospheric-Space Interactions Monitor (ASIM) experiment was deployed to the ISS on 2 April 2018. ASIM consists of two individual instruments:

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1. the Modular X-Ray and Gamma-Ray Sensor (MXGS) which utilizes a twolayer detector plane where the upper layer consists of a tiled array of 4 cm.× 4 cm, 5 mm thick CZT each with a 16. × 16 pixelated anode on a 2.5 mm pitch. Each individual detector is coupled to two XA-1.82 ASICs from Ideas (i.e. 128 ch/ASIC). Fully assembled, the entire detector plane comprises a total active area of 1024 cm.2 . The lower detector plane is comprised of an array of four 15 cm.× 15 cm.× 3.2 cm BGO bars, each with a separate readout giving an active area of 900 cm.2 . A coded aperture mask is mounted 30.3 cm above the detector plane to provide an imaging capability for high energy transients within the Earth’s atmosphere [109]. 2. the Modular Multi-Spectral Imaging Array (MMIA) is designed to monitor the Earth in the same region as the MXGS in order to capture and characterize Transient Luminous Events (TLEs) [58]. In this way the ASIM experiment is beginning to study the association between contemporaneous optical TLEs and high-energy TGFs in order to clarify their individual natures as well as to unmask the relationship between these two phenomena.

6.6 Solar Instrumentation So far ISRO has launched 3 missions making use of 5 mm thick, 4 cm.× 4 cm CZT crystals provided by GE medical devices (formerly Orbotech) for in situ characterization of the Lunar surface (Chandrayaan-1), observation of hard X-ray sources and transients (ASTROSAT-CZTI), and for solar observations in partnership with Russia. The ISRO contribution to the Russian CORONAS-PHOTON mission, RT-2, consisted of 3 GE CZT crystals [101]. Here two different imaging techniques were attempted (1) using a Fresnel zone plate and (2) a coded aperture imager. The mission launched on 20 January 2009 but was terminated in December of the same year impeding the science return of this instrument. More recently the Solar Orbiter [97] (10 February 2020-Present), an ESA Mclass mission with contributions from NASA, launched a CdTe detector plane based on the Caliste architecture that has been in development led by CEA with Le site du Centre national d’études spatiales (CNES) for over 15 years. The primary science target of the Spectrometer/Telescope for Imaging X-rays (STIX) instrument is to perform hard X-ray imaging spectroscopy of solar X-ray flares over the 4–150 keV energy range with a 7. angular resolution. The STIX [88] instrument makes use of the indirect Fourier transform imaging that has been utilized for this purpose since at least the early 1990s; the Hard X-ray Telescope (HXT) of the Yohkoh mission utilized a similar optical assembly but with a PSPC [87]. Similar to the Parker Solar Probe, the Solar Orbiter mission will make close passes of the sun, coming within 0.28 AU, in order to resolve processes within the photosphere and corona, investigate the origin of the coronal magnetic field and solar wind, the production of energetic particles in during solar eruptions and their interaction with

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the heliosphere, etc. Through multiple gravity assist maneuvers the Solar Orbiter probe’s orbital inclination will be raised to 33.◦ enabling the best view of the solar polar region yet achieved.

6.7 Instrumentation for Planetary Science After the launch of the Dawn mission (see Sect. 3.3) efforts to deploy a CdTe or CZT gamma-ray spectrometer or imager have not progressed rapidly. I am aware of a single program under development which proposes the use of CZT: Ambient-Temperature Imaging Gamma-Ray Spectrometer (TIGRS) [104]. Here thick pixelated CZT detectors would be utilized to form a Compton imager which could map elemental abundance distributions with higher precision than is possible with a simple non-imaging spectrometer. Given the success of CZT and CdTe in astrophysics additional development efforts may certainly be expected in the near future. Outside of the U.S. the ISRO flew a CZT based collimated spectrometer, the High Energy X-ray Spectrometer (HEX) instrument, for this purpose on the lunar observing mission Chandrayaan-1 that launched on 22 October 2008 and terminated less than 1 year later in August of 2009. The full detector plane made use of a 6 .× 6 array of 5 mm thick GE CZT modules, the same described earlier in Sect. 6.6 and Sect. 6.1. The objectives of the HEX mission were focused on Lunar volatile transport of .222 Rn and an attempt to trace this process through observation of the .210 Pb decay line (46.5 keV). Although the HEX instrument was not able to achieve this objective due to high backgrounds and a reduction in the mission duration [146], the HEX experience paved the way for the standardized CZT detector plane system that has supported ISRO missions over the last decade and is likely to see deployment on future ISRO missions (e.g. Daksha; see Sect. 6.1).

6.8 A Quick note on Polarimeters Most of the discussions thus far have focused on imaging spectrometers but I have neglected to cover the topic of hard X-ray polarimeters. There are a number of concepts and balloon-borne payloads that make use of CZT for the characterization of X-ray polarization from astrophysical sources, but none that have been deployed to LEO or beyond, the Hitomi SGD and ASTROSAT CZTI excepted. Many of these concepts use a grazing incidence optic to concentrate X-ray photons onto a low-Z detector, Si or a scintillator, which is surrounded by a pixelated CZT detector plane. The hard X-rays which undergo Compton scattering in the low-Z detector may then escape for detection at the periphery within the CZT. The measurement of the initial deposited energy due to the initial scattering event coupled with the detection and measurement of the energy of the outgoing photon

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in the CZT detector plane with the added positional information enables one to reconstruct the polarization vector of the source after the collection of many such events (e.g. XL-Calibur [4]). The development of instruments of this class can be expected to continue and it is conceivable that a mission dedicated to their deployment to LEO could occur within the next decade.

7 New Deployment Opportunities Over the last 20 years additional emphasis has been placed on improving access to space by a number of space agencies. I would argue that the JAXA and NASA have stood at the forefront of this effort and both have been aggressively expanding these programs not only for engineering and science payloads but as a public outreach and education tool as well. Within the scientific community there has been greater recognition that it is possible to achieve significant science within constrained payloads, though this requires a great deal of ingenuity and effort in order to compensate for the imposed constraints.

7.1 CubeSats Since their introduction in the early-2000s CubeSats have gradually gained popularity due to their low-cost and the opportunities they provide for education and outreach. The scientific potential of these systems has also been recognized by NASA and other space agencies worldwide fueling a boom in their deployment. CubeSat spacecraft are available from a number of different commercial vendors but are designed to a strict standard to enable low cost attachment as a ride-along payload or for flight to the ISS for eventual release. Each CubeSat adheres strictly to a 10 cm.3 form factor, i.e. 1U, and are commonly combined to produce 3U (10 cm.× 10 cm.× 30 cm) and 6U (10 cm.× 20 cm.× 30 cm) payloads. Depending on the vendor and mission requirements, scientific payloads may occupy up to 80–90% of the available volume. Most missions launched at present likely are accompanied by at least a few CubeSats. HaloSat was the first dedicated NASA astrophysics mission that utilized a CubeSat and was released from the ISS on 13 July 2018. HaloSat was a X-ray line mapping mission launched to probe emission from ionized Oxygen in hot halos surrounding nearby galaxies in an effort to assess the contribution of this region to the cosmological mass budget [82]. The success of this mission demonstrated that low-cost, targeted science investigations within small payloads and budgets is possible.

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It is also important note that a number of engineering and education payloads which have included CZT instruments as part of their payloads have also been deployed, in particular the Cosmic X-ray Background NanoSat (CXBN) 1 and -2 [67, 127] which were launched in 2012 and 2015, though results on their measurements have, to my knowledge, not yet been published. Since that time a number of other CubeSats bearing CZT instruments have been launched, most recently Sharjah-Sat-1 [83] (3 January 2023), which will use a single 25.4 cm square, 3 mm thick CZT with a unique segmented anode pattern in conjunction with a collimator with the stated objective to characterize the hard X-ray component of the solar corona as well as monitor known hard X-ray astrophysical sources. With the expansion of launch opportunities that CubeSats afford together with the high-efficiency and relaxed thermal requirements that CZT and CdTe offer, the deployment of more small-scale instrumentation for a wide variety of cross-cutting science objectives using these materials is a near certainty.

7.2 SmallSats SmallSats are a larger class of ride-along payload which have been under development for the last 15 years and are now routinely launched as well. The forerunner of the SmallSat can be traced to the “university-class” program that NASA initiated in 1989 for the deployment of low-cost satellites in collaboration with institutions of higher education. One such mission, High Energy Transient Explorer 2 (HETE-2) launched on 9 October 2000 to explore the soft (2–25 keV) and hard (30–400 keV) X-ray regime was dedicated the study of GRBs and continued operation until 2007 [122]. Subsequently, JAXA, then NASA began introducing standardized ports on the payload adapter ring which serves as the mechanical interface between the launcher and primary payload. These ports enable the mounting of additional sub-payloads, i.e. SmallSats, within the surplus space between the rocket and the primary payload. One of the earliest series of SmallSat launches was carried out by JAXA with the launch of the Hayabusa-2 mission on 2 December 2014 in this manner. A more recent SmallSat example is MoonBEAM [72] which carries a simple non-imaging scintillator system similar to that of the BATSE and the Gamma-ray Burst Monitor (GBM), and was selected for a Phase A study expressly for the detection of transient X-ray events. The key difference between MoonBEAM and previous scintillator based missions is that it will be injected into a highly elliptical cis-Lunar orbit, in some ways similar to that used for the ISEE-1 satellite, to enable near all-sky coverage during the observing runs of Gravitational Wave detectors, if it is ultimately selected for launch. A major reason for the serious consideration of MoonBEAM for launch rests with the widespread recognition that small missions can enable follow-up observations and thereby contribute to the advancement of our fundamental understanding of these short-duration phenomena.

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For the same reason, and with the advantages that CZT offers for resourceconstrained payloads, and its demonstration on small CubeSat payloads, the deployment of these materials on a SmallSat mission, e.g. the HREXI effort described earlier in Sect. 6.1, is highly likely in the near future.

8 Some Current Science Drivers and New Opportunities Each decade the astronomical, planetary science, and heliophysics communities come together to define objectives and funding priorities for the next 10 years which is used by the federal funding agencies: NASA, National Science Foundation (NSF), etc. to define implementation strategies and policies to realize as many of the community’s objectives as possible within budget constraints. The last decadal survey for astrophysics heavily emphasized the need for new instrumentation and facilities [103] for the study of time domain multi-messenger astrophysics (TDAMM) phenomena, including GRBs and supernovas (SNs). This was motivated in no small part by the first detection of Gravitational Waves in 2016 [5] and their known connection to the mergers of compact objects (e.g. BHs and NSs) which, in some cases, results in an observable GRB. The additional need for enhanced followup capabilities exceeding those of the Swift mission and other currently operational payloads has been highlighted by the sheer number of gravitational wave detections (see Fig. 7) and the dearth of corresponding EM counterpart detections. In fact, the simultaneous detection of a gravitational wave event and identification of a EM counterpart has only been achieved once. The event, designated GW170817, was identified the merger of two Neutron Stars or a NS-NS merger. Approximately 1.7 s after the detection of the GW signature by 2 LIGO stations (Hanford, WA and Livingston, LA) and 1 Virgo station (Santo Stefano a Macerata, Italy) the INTEGRAL observatory and the Fermi-GBM, a more modern incarnation of the scintillator detector systems used ubiquitously in the search for GRBs since their discovery in the 1970s (see Sect. 1.2) [6]. These detections kicked off a massive campaign of follow-up observations that resulted in additional detections across the EM spectrum. The source of the EM emissions observed are consistent with the decay of r-process nuclei that are expected to arise during a NS-NS merger event and was consistent with the GW signature. When the joint LASER Interferometer Gravitational-Wave Observatory (LIGO)Virgo-Kamioka Gravitational Wave Detector (KAGRA) observing run resumes in mid-2023, it is plausible, even likely, that the current suit of instruments in orbit will, once again, enable such observations. However, due to the fleeting nature of these events, along with the opportunity they provide to probe the physics of extreme environments, i.e. strong gravitational fields, neutron star equations of state, etc. there is a strong motivation to improve X-ray monitoring capabilities on orbit. Although not covered here in any detail, there are other transient phenomena of unknown origin, e.g Fast Radio Bursts (FRBs) only recently discovered in

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Fig. 7 The minimum cumulative number of GRBs detected since their discovery in 1967 with the contributions of individual instruments derived the HEASARC provided data tables grbcat, hete2grb, fermi-gbm and pvogrb [2], as well as the 3rd Swift GRB Catalog [91] with removal of duplicate entires common to 2 or more of these catalogs. Though the impact of the BATSE instrument on our sample and understanding of GRBs was immense the much smaller sample acquired with BeppoSAX was equally impactful highlighting the value of followup observation. Plotted alongside the GRB detections are the number of Gravitational Wave events (magenta; derived from the “confident” GWTC catalog for LIGO/Kagra/Virgo over all observing runs up to the present (O1-O3) [3, 34]). Multi-wavelength followup and high-energy telescopes will play a significant role in the study of these events in the years to come.

2007 [92], which will require robust multi-wavelength follow-up capability for characterization and eventual explanation. The addition of new ground-based facilities is the coming decade are also expected to vastly expand the transient monitoring capability across the EM spectrum, e.g. Canadian Hydrogen Intensity Mapping Experiment (CHIME) [33] in radio, the Vera Rubin telescope (formerly the Large Synoptic Survey Telescope (LSST)) [76] in visible/IR, a new generation of IACTs and wide-field TeV instruments [7, 9]. This will provide additional opportunities as well as significant challenges for multi-wavelength counterpart searches which will require additional monitoring capability in the X/.γ -band covered by CZT detectors in order to fully exploit the opportunities presented not only by the new GW detection capabilities, but the flood of data that can be expected in the next decade and beyond for a wide variety for transients.

9 Conclusions Over nearly 45 years CdTe, then CZT detectors of increasing complexity and volume have been incorporated onto payloads for a wide-range of scientific investigations, ranging from the observation of phenomena in the Earth’s atmosphere, to

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the study of solar flares in our own Sun, and to uncover the mysteries surrounding the end states of stellar evolution, the history of star formation and nucleosynthesis, as well as the growth of black holes and for the study of extreme physical processes that cannot be replicated in laboratories on Earth. The evolution and maturation of CZT and CdTe technologies over the past 20 years in particular have given the scientific community ample experience in their operation and proven that they may be reliably deployed into the space environment under a wide variety of conditions. The breakthroughs enabled by the last generation of CZT and CdTe wide-field monitors and focusing telescopes has paved the way for future missions ranging from focused CubeSats to large next-generation wide field monitors. These new instruments promise to play a key role in a wide range of investigations that touch and advance every facet of the space sciences, extending from processes taking place in our own atmosphere, to the exploration of the solar system, and all else the lies far beyond.

10 Glossary and Acronyms ANS AGN ASAT ASCA ASIC ASI ASIM AXAF BAT BATSE BeppoSAX BGO BH BLP CCD CEA CHIME CNES CORSA-b COSI CPG CGRO CXBN CXO CZT CZTI

Astronomical Netherlands Satellite Active Galactic Nuclei anti-satellite weapon Advanced Satellite for Cosmology and AStrophysics application specific integrated circuit Agenzia Spaziale Italiana Atmospheric-Space Interactions Monitor Advanced X-ray Astrophysics Facility Burst Alert Telescope Burst and Transient Source Experiment Satellite italiano per Astronomia X bismuth germanate black hole boron loaded plastic charge coupled device Commissariat à l’énergie atomique et aux énergies alternatives Canadian Hydrogen Intensity Mapping Experiment Le site du Centre national d’études spatiales Cosmic Radiation Satellite Compton Spectrometer and Imager co-planar grid Compton Gamma-Ray Observatory Cosmic X-ray Background NanoSat Chandra X-ray Observatory CdZnTe CZT Imager

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CXB DM DOD DSSD EAS EM ESA EUV FC FFT FoV FOXSI FRB FWHM FWHI GALCIT Galileo-SSI GBM GC GE GEMS Giotto-HMC GRaND GRB GRIS GSFC GW HEAO HEASARC HERO HEFT HETE-2 HEX HEXITEC HPD HPGe HREXI HRI HST HXI HXT JAXA JPL KAGRA

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cosmic X-ray background Detector Module Department of Defense Double-Sided Strip Detector Extensive Air Shower Electromagnetic European Space Agency Extreme Ultraviolet Framing Camera fast Fourier transform Field of View Focusing Optics X-ray Solar Imager Fast Radio Burst Full-Width Half-Maximum Full-Width Half-Intensity Guggenheim Aeronautical Laboratory of the California Institute of Technology Galileo solid state imager Gamma-ray Burst Monitor galactic center General Electric Gamma Ray Environment Sensor Giotto Halley Multicolour Camera Gamma Ray and Neutron Detector Gamma-Ray Burst Gamma-Ray Imaging Spectrometer Goddard Space Flight Center Gravitational Wave High Energy Astrophysical Observatory High Energy Astrophysics Science Archive Research Center High Energy Replicated Optics High Energy Focusing Telescope High Energy Transient Explorer 2 High Energy X-ray Spectrometer High Energy X-ray Imaging Technology Half-Power Diameter High Purity Germanium High Resolution Energetic X-Ray Imager High Resolution Imager Hubble Space Telescope Hard X-Ray Imager Hard X-ray Telescope Japan Aerospace Exploration Agency Jet Propulsion Laboratory Kamioka Gravitational Wave Detector

Space Applications of CdZnTe and CdTe Detector Systems: Past, Present and Future

IACT IBIS IDeF-X InFOCμS ISGRI ISRO INTEGRAL ISEE ISS LAD LIGO LDB LEO LSST MCP Mfg. MIDEX MMIA MPI MXGS NASA NASA-JPL NAAP NIVR NSF NuASIC NuSTAR NS ORDCIT OSO PICsIT PoRTIA PC PSPC R⊕ SAS SAS-A SD SGD SIS SL2-XRT SMEX SRTM

Imaging Atmospheric Air Cherenkov Telescope Imager on Board the INTEGRAL Satellite Imaging Detector Frontend International Focusing Optics Collaboration for μ-Crab Sensitivity INTEGRAL Soft Gamma-Ray Imager Indian Space Research Organization International Gamma-Ray Astrophysics Laboratory International Sun-Earth Explorer International Space Station Large Area Detector LASER Interferometer Gravitational-Wave Observatory long-duration balloon flight low Earth orbit Large Synoptic Survey Telescope Microchannel Plate Manufacturer Medium-Class Explorer Mission Modular Multi-Spectral Imaging Array Max Planck Institut Modular X-Ray and Gamma-Ray Sensor National Aeronautics and Space Administration NASA Jet Propulsion Laboratory Netherlands Agency for Aerospace Programs Nederlands Instituut voor Vliegtuigontwikkeling en Ruimtevaart National Science Foundation NuSTAR ASIC Nuclear Spectroscopic Telescope Array Neutron Star Ordinance-California Institute of Technology Orbiting Solar Observatory Pixelated Imaging CsI Telescope Piggyback Room Temperature Instrument for Astronomy proportaional counter position sensitive proportional counter Earth radii Small Astronomy Satellite Small Astronomy Satellite A Spectroscopic Detector Soft Gamma-Ray Detector Solid State Imaging Spectrometer Spacelab 2 X-ray Telescope Small Mission Explorer Shuttle Radar Topography Mission

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STS STIX SN SNR SVOM SXI SXS TDRS TDAMM TGF TI TIGRS TLE TSM UCSD UNH UVOT VHE MDU MOC MSL NeXT ULDB VIR Voyager-ISS VPCCD XIS XRISM XRT XMM XMM-Newton WD WFC WF/PC

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Space Transportation System (i.e. The Space Shuttle) Spectrometer/Telescope for Imaging X-rays supernova supernova remnant Space-based Astronomical Variable Object Monitor Soft X-ray Imager Soft X-ray Spectrometer Tracking and Delay Relay Satellite time domain multi-messenger astrophysics Terrestrial Gamma-Ray Flash Texas Instruments Ambient-Temperature Imaging Gamma-Ray Spectrometer Transient Luminous Event Transient Source Monitor University of California, San Diego University of New Hampshire Ultraviolet/Optical Telescope Very High Energy Modular Detection Unit Mission Operation Center mean seal level New exploration X-ray Telescope ultra-long duration balloon flight Visible and Infrared Spectrometer Voyager imaging science subsystem virtual phase CCD X-ray Imaging Spectrometer X-Ray Imaging and Spectroscopy Mission X-Ray Telescope X-Ray Multi-Mirror Mission X-Ray Multi-Mirror Mission Newton White Dwarf Wide-Field Camera Wide Field/Planetary Camera

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Germanium Detectors for MeV Gamma-Ray Astrophysics with the Compton Spectrometer and Imager Jacqueline Beechert, Hadar Lazar, and Albert Y. Shih

1 The MeV Gap in Astrophysics Accessing the rich scientific potential of the MeV bandpass is of high priority in the astrophysics community. Home to a wealth of astrophysical mysteries, including determining the nature of Galactic positrons, measuring emission from Galactic nucleosynthesis, and performing novel polarization measurements of gamma ray bursts (GRBs) and compact objects, decades of astrophysics experiments have been devoted to exploring this energy regime (refer to Sect. 7 for a brief review of a few of these goals). In this chapter, we describe the Compton Spectrometer and Imager (COSI), previously a balloon-borne instrument now funded as a future NASA Small Explorer space mission, which uses state-of-the-art high purity germanium detectors to tackle the challenges of observing in this bandpass. Spectroscopic, imaging, and polarization studies of MeV photons have historically suffered from poorer sensitivity compared to those in adjacent energy ranges. In astrophysics, this range is accordingly referred to as the “MeV gap” (0.1–10 MeV) [1, 2]. Figure 1 shows the diminished sensitivity of astrophysics instruments operating within the MeV gap compared to missions which detect photons of lower and higher energies. Poorer sensitivity in the MeV gap is attributed to: 1. Low interaction cross-sections 2. High instrumental background

J. Beechert () · H. Lazar Space Sciences Laboratory, University of California, Berkeley, CA, USA e-mail: [email protected]; [email protected] A. Y. Shih NASA Goddard Space Flight Center, Greenbelt, MD, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_10

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Fig. 1 The “MeV gap” between 0.1–10 MeV is characterized by poor continuum sensitivity compared to adjacent energy ranges. Continuum sensitivity is a measure of minimum detectable flux from a gamma-ray source. Image is from [3]

3. Instrumental constraints Photon detection is predicated on interaction with matter. The cross-section of this interaction is a measure of probability which is dependent on both photon energy and the properties of the detecting material. For example, in silicon (atomic number .Z = 14) and germanium (.Z = 32), two commonly used materials for semiconductor detectors, the overall interaction cross-section reaches a minimum near an incident photon energy of a few MeV (Fig. 2), squarely in the MeV gap. Figure 2 also demonstrates that the dominant interaction mechanism between .∼ 0.1 − 10 MeV is Compton scattering. Photons typically Compton scatter between two and seven times in the detector volume, each at a different location and with changing energy. Sophisticated event reconstruction algorithms are required to chronicle this complicated sequence of Compton scatters. In recognition of Compton scattering as the dominant interaction mechanism in this energy range, detectors are developed to induce and track the Compton scattering path of photons throughout the instrument; refer to Sect. 3 for an overview of this operating principle. Additionally, MeV astrophysics missions are susceptible to significant background contamination from nuclear excitation and de-excitation of instrument materials. This is often referred to as “instrumental activation.” Instrument materials, including the HPGe detectors themselves and surrounding components, can be excited to higher energy states, i.e. are “activated,” by incident high-energy particles from space, often cosmic rays. The activated materials subsequently decay on the time scale of desired measurements via the emission of a gamma-ray.

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Fig. 2 Attenuation of photons in germanium and silicon, two common materials for semiconductor detectors used for gamma-ray detection. The MeV gap is dominated by Compton scattering and encompasses the minimum overall interaction cross-section near a few MeV. Attenuation data are from NIST XCOM [4]

The gamma-rays from these background nuclear decays lie in the MeV bandpass and must be distinguished from signal photons, further underscoring the uniquely difficult conditions of observing in this regime. Discerning the background activation gamma-rays from astrophysical gamma-rays often involves a combination of substantial simulation time, uncertain estimations of high-energy particle fluxes in the instrument’s orbit, and dedicated observation time of background irradiation on gamma-ray instruments. Machine learning methods may also be used to separate signal and background. Finally, astronomical instruments are subject to practical constraints which hinder their ability to detect photons in the MeV range. MeV photons are of sufficiently high energy to Compton scatter non-negligible distances and even pair produce, creating tracks on the order of several centimeters which must be fully contained in the detector volume. Creating arbitrarily large detectors, however, is not without cost. It is difficult to manufacture large solid state detectors, and balloon and satellite launch platforms face strict upper limits on mass. Additionally, typical orbiting altitudes of MeV astrophysics instruments are plagued by atmospheric background contamination. Particle and photon interactions in the Earth’s atmosphere cause it to emit intensely in the gamma-ray bandpass. This atmospheric “glow” in gamma-rays is called Earth albedo radiation. Balloon missions, which typically float at altitudes of approximately 30–40 km in the Earth’s atmosphere, require heavy shielding to reject these events. Satellite orbits avoid this significant source of background by their increased distance from the Earth albedo radiation. Carefully curated instrument designs using semiconductors, scintillators, gaseous detectors, electron-tracking silicon wafers, and more have been developed to address the immediate need for sensitive measurements of MeV gamma-rays. The following sections describe how COSI uses germanium detectors to perform the high-resolution spectroscopic, imaging, and polarization analyses required to close the MeV gap. A discussion about germanium detectors, with comparison to adjacent detector technologies, is provided in Sect. 2, followed by an introduction to

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the general operating principle of Compton telescopes in Sect. 3. Sect. 4 describes the COSI instrument in more detail and is followed by an overview of its calibration procedures (Sect. 5), metrics of instrument performance (Sect. 6), and finally scientific achievements as a balloon-borne germanium Compton telescope (Sect. 7).

2 High-Purity Germanium Detectors Germanium semiconductor detectors—particularly high-purity germanium (HPGe) detectors—have key advantages for making breakthrough observations in the MeV gap. Not only can HPGe detectors be fabricated with large volumes and excellent energy resolution, but modern advances in contact fabrication enable the fine segmentation of such large-volume HPGe detectors to locate individual energy depositions in 3D, not just 2D. Even one of germanium’s limitations—its merely good and not excellent stopping power—can be considered an enabling feature for certain types of instruments. Energy Resolution As with other semiconductor detectors, germanium detectors achieve excellent energy resolution thanks to the large number of electron-hole pairs that are created when energy is deposited. Among semiconductors, germanium has the lowest average energy (2.96 eV) to create an electron-hole pair, so depositing 1 MeV creates .∼340,000 pairs. The intrinsic relative uncertainty of this number would already be very low if Poisson statistics were appropriate, but because the creation of electron-hole pairs is not statistically independent, the actual variance is smaller than Poisson variance by an empirical ratio called the Fano factor [5]. This low intrinsic uncertainty is just one component of the energy resolution, which is typically dominated by other sources of noise (e.g., from readout electronics). However, there are some instruments that are able to achieve Fano-limited energy resolution. By contrast, scintillator detectors produce far fewer scintillation photons for the same amount of energy deposited, with .∼15 eV per scintillation photon on average for even the brightest scintillators. There are also inefficiencies and losses in the detection of those scintillation photons (e.g., by a photomultiplier tube). For a deposition of 1 MeV in the scintillator, there may be only .∼10,000 photoelectrons produced at the input of the corresponding photomultiplier tube. Finally, there is no analogue of the Fano factor: the relative uncertainty of the number of photoelectrons behaves as predicted by Poisson statistics. Consequently, scintillator detectors have energy resolutions that are at least an order of magnitude worse than germanium detectors. Finely Segmented Large Volumes Semiconductor detectors are typically limited to thicknesses of .∼1 cm at most because the achievable impurity levels are too high to prevent breakdown when applying high-voltage bias. HPGe detector material is fabricated in a process

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specific to germanium called zone refining where impurities are “swept” out, resulting in one to two orders of magnitude lower impurity levels [6]. A HPGe detector can then reach a thickness of multiple centimeters in the bias direction, and depending on the the detector geometry, can have a volume of hundreds of cubic centimeters. Other semiconductor detectors would be able to achieve such volumes only through two- or three-dimensional arrays of smaller detectors (e.g., each with a volume of .∼1 cc), with correspondingly greatly increased design complexity and unavoidable passive material between the detectors that would degrade the quality of measurements. Furthermore, the blocking contacts for such large-volume detectors can now be fabricated using amorphous germanium (or silicon), instead of traditional techniques such as lithium-drifted contacts. The excellent blocking properties of amorphous-germanium contacts facilitate fine electrical segmentation of the contacts akin to the pixelization that is possible with thin semiconductor detectors. The HPGe detectors on COSI leverage this advantage by using orthogonal strip contacts on opposite faces to recover the full 3D location of each energy deposition. As mentioned previously, such full 3D information could alternatively be recovered through a massive 3D array of pixelated non-germanium semiconductor detectors, albeit at greatly increased design complexity. The large volume attainable in a single HPGe detector compares favorably to the typical large scintillator detector (e.g., .3 × 3 crystals) and it is simpler to achieve volumes of thousands of cubic centimeters through arrays of scintillator detectors than arrays of HPGe detectors, given the associated electronics. However, such an array of scintillator detectors would not reap the other benefits of HPGe detectors. Cryogenic Operation Germanium’s excellent energy resolution is coupled with its most readily apparent limitation: germanium detectors typically must be operated at cryogenic temperatures. The need for such low temperatures is that the bandgap energy of germanium is only 0.7 eV, one of the smallest for a semiconductor. Accordingly, germanium at room temperature continuously generates electron-hole pairs from thermal motion alone, and the resulting thermal leakage current renders the detector inoperable. Most non-germanium semiconductor detectors can be operated at room temperature, although they would typically benefit from reduced noise if cooled to 0.◦ C or colder. In a laboratory setting, germanium detectors are typically kept cold using liquid nitrogen, and thus are operated at a temperature close to 77 K. In space, missions such as RHESSI [7] and INTEGRAL [8] have demonstrated the effectiveness of using a mechanical cryocooler to maintain germanium detectors at liquid-nitrogen temperatures, which allows for mission durations of over a decade thanks to the lack of an expendable resource. Stopping Power The stopping power of a gamma-ray detector is primarily a function of the mass of the detector material, but it also depends on the atomic number (Z) because higherZ materials are more likely to absorb photons rather than allow them to Compton

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scatter and potentially escape the material. Germanium has the relatively low Z of 32 compared to elements in other materials used for gamma-ray detectors—e.g., the iodine in sodium-iodide detectors has a Z of 53—and thus for the same mass, germanium’s efficiency for fully stopping an incident gamma-ray is lower. Yet, this slightly lower photopeak efficiency can be mitigated by the large achievable volumes of HPGe detectors, and regardless may be a worthwhile trade-off for the excellent energy resolution. Specifically, compared to other materials, gamma-rays will tend to Compton scatter in germanium. Moreover, the Compton-scattered photon is more likely to travel an appreciable distance or scatter again prior to being absorbed. While this behavior does negatively impact the photopeak efficiency, it turns out to be an enabling feature for Compton telescopes, which are described in the next section.

3 Principles of Gamma-Ray Detection in Compton Telescopes As photons propagate through the detector volume of Compton telescopes, the deposited energies and locations of each interaction site are recorded. The energy of a Compton-scattered photon (.E  ) is given by the Compton equation: E =

.

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where .E0 is the initial energy of the photon, .me c2 is the rest energy of the electron, and .cos φ is the cosine of the Compton scattering angle. The operating principle of a “compact” Compton telescope (CCT) uses the measured energies and locations of at least two interaction sites to confine the origin of the propagating photon to a cone defined by .cos φ; refer to Sect. 3.1 for an explanation of the “compact” distinction. Figure 3 illustrates this principle with an example case of only two interaction sites: an incident photon Compton scatters in the detector volume at location .r1 , deposits energy .E1 , and subsequently deposits energy .E2 at location .r2 in a final photoabsorption interaction (i.e., .E2 is equal to .E  in Eq. 1). The energy of the incident photon is reconstructed as the sum of the deposited energy, .E0 = E1 + E2 . The origin is constrained to a circle on the sky tracing the base of the Compton cone, which is defined by:

.

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Fig. 3 Principle of Compton telescopes. Left: Illustration of a gamma-ray event with two interactions measured by detectors with 3D position measurement capabilities (COSI, a CCT, is shown). Compton scattering detectors can reconstruct the Compton scattering angle (.φ) and the azimuthal scattering angle (.η). Image from [9]. Right: The intersection of overlapping event circles marks the source location

The intersection of overlapping circles on the sky, also called “event circles,” from multiple incident photons localizes the source (Fig. 3). Optionally tracking the recoil electron of a Compton scatter provides additional kinematic information which can reduce the circles to arcs on the sky. Event reconstruction in CCTs is complicated by the fact that the timing resolution of the HPGe detectors is too coarse to determine the sequence of interactions with absolute time tags (.∼ 10 ns resolution for interactions which occur on sub-nanosecond scales). As such, the most likely gamma-ray path is determined through interaction probabilities and kinematics. The Klein-Nishina differential cross-section (Eq. 3; [10]) defines the probability of a Compton interaction given its measured scattering angle and energy. It is also dependent on photon polarization, though this is not used in the event reconstruction.  2   r02 E  E E dσ 2 2 − 2 sin φ cos η = + . 2 E E E d

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Additionally, given the properties of the detector material and energy of the gammaray, the probability that the traveling gamma-ray traverses the distance between any two potentially sequential interactions limits the number of possible paths. Further constraints on the order of interactions are derived from redundancy between kinematic and geometric determinations of the Compton scattering angle: the correct order of interactions is that which gives the same scattering angle, within uncertainties [11, 12]. A Bayesian approach [12, 13], a random forest of decision trees, and shallow neural networks are also being developed for event reconstruction in Compton telescopes. For more information about these techniques and the principles of gamma-ray detection in Compton telescopes, refer to [2, 12, 14].

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3.1 Comparison to Other Gamma-Ray Instruments There are advantages and disadvantages of the CCT design compared to other commonly employed gamma-ray instruments, including the “classic” Compton telescope, the coded-mask imager, and the Laue lens. Both the “classic” Compton telescope and CCT designs perform single-photon reconstruction. A “classic” Compton telescope (e.g. the COMPTEL instrument on-board NASA’s CGRO satellite [15]) Compton scatters a photon once in a lowZ scattering plane positioned .∼2 m above a high-Z absorber plane, where the remaining energy is deposited via photoabsorption. The classic telescope is simpler in design but has lower efficiency than the CCT, as it can only detect photons which Compton scatter once and at a small enough angle to be detected in the absorber plane. A coded-mask imager (e.g. the SPI instrument on-board ESA’s INTEGRAL satellite [8]) reconstructs sources through shadow patterns cast by incident photons on a plane of semiconductor detectors (HPGe) positioned below a high-Z (tungsten) mask. Coded-masks boast simplicity in design and event reconstruction, as there is only one interaction per event. This simplicity sacrifices sensitivity to low flux gradients and intrinsic background rejection techniques in CCTs, which can boost sensitivity by factors of .∼5–10. Lastly, Laue lens instruments use Bragg diffraction to focus gamma-rays onto a detector plane. They have low background due to small collecting areas and achieve remarkable arc-second angular resolution, but strict diffraction requirements severely limit their energy range and field of view and require prohibitively long focal lengths of .> 10 m. Thus, only the CCT can perform single-photon reconstruction, wide field-ofview imaging of low-gradient emission, and intrinsically suppress background events. A comprehensive review of Compton telescopes in gamma-ray astrophysics is provided in [16], and a review of various telescope concepts in the field is provided in [2].

4 The Compton Spectrometer and Imager COSI is an MeV gamma-ray CCT designed to determine the nature of Galactic positrons, measure emission from Galactic nucleosynthesis, and perform novel polarization measurements of gamma-ray bursts (GRBs) and compact objects. It was originally deployed as a scientific balloon mission [17] and is being upgraded to a satellite mission for launch in 2027 [18]. Operating COSI at balloon (.∼33 km) or satellite orbits (low-Earth orbit .∼500 km) is necessary because MeV photons are attenuated in the atmosphere and cannot be detected on the ground. The HPGe detector volume of the balloon instrument (Fig. 4), the advantages of which uniquely

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Fig. 4 Top left: One of COSI’s twelve HPGe detectors. The reflection in the mirror shows the orthogonal strips on the opposite side of the detector. Image from [19]. Top right: Stack of COSI’s HPGe detectors which form the full detector volume. Image from [20]. Bottom left: The COSI cryostat maintains the detectors at pressures of .10−6 torr. The cryocooler in the foreground cools the detectors to .∼84 K. Image from [20]. Bottom right: The fully assembled COSI gondola before launch in 2016. Image courtesy of the COSI collaboration

enable COSI to pursue its scientific objectives, is described in this section1 . The satellite design will be very similar.

4.1 COSI HPGe and instrument Design COSI’s detector volume is comprised of twelve double-sided cross-strip HPGe detectors (Fig. 4). The detectors are .8 × 8 × 1.5 cm3 and were fabricated using 1 This

section draws heavily from the publication [20]: Beechert, Lazar, et al., Calibrations of the Compton Spectrometer and Imager, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Volume 1031, 2022, 166510, ISSN 0168-9002, https://doi.org/10.1016/j.nima.2022.166510.

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the Lawrence Berkeley National Laboratory’s amorphous Ge contact technology [21]. Orthogonally oriented aluminum strip electrodes are deposited on opposite sides of the detector. The 37 strips on each side (888 total over all detectors) are of 2 mm strip pitch and the gap between each strip is 0.25 mm. This gap achieves a balance between small gaps, which minimize the risk of losing charge carriers that fall between strips, and large gaps, which improve energy resolution through decreased strip capacitance. Leakage current from events close to the edge of the detector is collected by a 2 mm-wide guard ring that surrounds the active area of each detector face. Note that the COSI satellite instrument will have sixteen of these detectors with 64 strips per side for enhanced effective area and angular resolution, respectively. The intersection of orthogonal triggered strips defines the x–y position of a photon interaction [22]. The depth of the interaction in the detector (z-position) is computed from the timing difference between electrons collected on the positively biased side (anode) and the holes collected on the grounded side (cathode) of the detector. Sect. 5.5 explains the conversion from timing to depth in more detail. Overall, the orthogonal strip electrodes have a 3D position resolution, defined as the product of the .x−, .y−, and .z−position resolutions (.∼2, .∼2, and .∼0.5 mm, respectively), of approximately 2 mm.3 [23]. The detectors are over-depleted with bias voltages between 1000 V and 1500 V. The high-voltage side is AC-coupled and accordingly referred to as the “AC side” (anode), while the low-voltage side is referred to as the “DC side” (cathode). To limit the effect of electronic noise, coincident triggers on the AC and DC sides are required to trigger the readout. Since launching the instrument with consumable liquid nitrogen would limit the mission duration and add considerable weight to the instrument payload, the detectors are cooled by a Sunpower CryoTel CT mechanical cryocooler (.∼26 cm long, .∼8 cm diameter; [24]) to approximately 84 K. The aluminum cryostat thermally isolates the detectors and maintains them at a pressure of approximately 10.−6 torr (Fig. 4).

5 Calibrations Robust calibrations are required to fully exploit the advantages afforded by HPGe detectors. This section (see footnote 1) details the calibration procedures which convert raw data from the COSI detectors into quantities with physical units, which can then be readily interpreted for the purposes of instrument performance or scientific analysis. A series of necessary corrections arising from effects intrinsic to the detectors, electronics, and the external environment are described as well. Each of these steps is essential to the end product: gamma-ray events whose energies and origins have been determined with the high resolution characteristic of HPGe detectors. While these procedures were developed specifically for the COSI instrument, the underlying principles are transferable to other applications. All electronic pulse-

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heights must be converted to energy, for example. The observed influence of temperature on COSI’s readout electronics may affect similar laboratory setups (e.g., see [25] for an alternative method of correcting temperature dependence in gamma-ray spectra from NaI scintillators). Thus, this section presents a calibration pipeline which can be adapted to an instrumentalist’s particular needs.

5.1 Energy Calibration Energy calibration defines the conversion from electronic readout units (e.g. ADC) to physical units (e.g. keV). This conversion is unique to each strip electrode, as COSI’s 888 strips are read out individually by the data acquisition system. There are variations in gain, threshold, and other electronic considerations which differentiate the strips’ individual calibrations and prohibit a global conversion. To achieve the required individual treatment, each strip is illuminated with radioactive sources that emit gamma-ray lines of known energy across COSI’s energy range. Each strip records a spectrum of pulse heights in response to the radiation. The photopeaks are fit in ADC space (the pulse heights) with a Gaussian, lower-energy continuum, and a linear background model. The fitting algorithm returns the centroid value of each fitted peak in ADC and matches it with the corresponding known, true photopeak energy in keV. The centroid energy versus ADC relation for each strip is fit with a polynomial that defines the desired relationship between pulse height and energy. While the centroid of the photopeak defines the energy calibration, the fullwidth half maximum (FWHM) of each photopeak defines the single-strip, energydependent energy resolution of the instrument. The “single-strip” distinction is important when considering the spectral capabilities of the HPGe detectors themselves against the spectral capabilities of the instrument overall. The photopeaks recorded on individual strips measure the signals induced by charge carriers in individual HPGe detectors and their respective electronic readouts. Photopeaks from spectra of fully reconstructed Compton events, namely those reconstructed from multiple Compton scatters potentially spanning several detectors, are additionally affected by subsequent calibrations and the quality of the event reconstruction itself. As a result, the single-strip resolution discussed here is a more reliable proxy of the performance of the HPGe detectors themselves, compared to that of the full COSI instrument (Sect. 6.1). The single-strip spectral resolution of COSI is given as the ratio of the FWHM of the .137 Cs gamma-ray line to its photopeak energy of 661.7 keV. In 2016 and 2020 calibration data, COSI had an average spectral resolution of .0.49 ± 0.01% on the AC side and .0.47 ± 0.01% on the DC side. Figure 5 demonstrates the dependence of COSI’s single-strip energy resolution on photon energy E. Below 1 MeV, the energy resolution is dominated by electronic noise and is approximately independent of photon energy. Accordingly, we expect the percentage energy resolution to scale as .1/E. Indeed, fitting the data points of percentage energy resolution versus energy with a power law gives a power law index .k = −0.96, matching expectations of dominant electronic noise in COSI up to about 1 MeV.

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Fig. 5 Single-strip energy resolution (FWHM) as a function of energy in 2016 and 2020 energy calibrations. The fitted power law exponent .k = −0.96 is consistent with expectations of dominant electronic noise in COSI’s detectors. Image from [20]

5.2 Temperature Dependence of the Readout Electronics Though not intrinsic to HPGe detectors, an important consideration during operation is that the accompanying electronic readout system may exhibit a temperature dependence. COSI’s preamplifier boards were observed to shift pulse-height spectra by up to 0.5 keV/.◦ C at 661.7 keV in laboratory calibrations [3], displacing recorded photopeak energies from their true values. Correcting the dependence is therefore critical to preserving HPGe detectors’ excellent energy resolution. A linear relationship between preamplifier temperature and ADC peak location was determined for each strip, yielding a precise correction tailored to each strip’s individual readout. The correction reduced the difference between measured and true line energy from 0.5 to 0.1% [3]. Experimentalists should be mindful of how ambient conditions may affect their chosen electronic readout and in turn, the interpreted performance of the detectors. Dedicated calibration time at controlled temperatures would greatly benefit this effort.

5.3 Cross-Talk Correction An additional deleterious electronic effect is “cross-talk,” which refers to electronic interactions between a strip and its neighbors that affect the measurement of charge on that strip. For COSI, a fraction of the events on a strip are affected by cross-talk and register more charge than was actually collected, which creates a “bump” in the higher-energy tail of the photopeak (Fig. 6). Correcting this offset between true and enhanced energy is necessary for accurate event reconstruction and spectral analysis. For COSI, the spurious enhancement in measured charge due to cross-talk is strongly correlated with corresponding enhancements in the neighboring strips,

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Fig. 6 The cross-talk influence of neighboring strip electronics enhances the energy recorded on nearby strips. Left: The resulting enhancement is visible at higher energies in an uncorrected .137 Cs spectrum. Right: Applying a linear correction removes the enhancement. Images are from [3]

and this relationship is carefully calibrated. The effect of cross-talk can then be subtracted from the measured charge in a strip using the information from the neighboring strips [3]. Figure 6 demonstrates how applying the cross-talk correction removes the unwanted enhancement at .∼670 keV and restores the spectrum to its expected appearance with one Gaussian photopeak at 661.7 keV.

5.4 Strip Pairing The x–y position of an interaction is determined using the triggered AC- and DCside strips in a process called strip pairing [26]. Strip pairing is straightforward if there is only one interaction in a detector: the x–y position is the point at which the orthogonal AC- and DC-side strips intersect. As the number of interactions increases, however, so does the number of candidate interaction locations. The correct solution matches the AC- and DC-side strips that record the most similar energy; neglecting small differences in recorded charge from the effects of charge carrier transport (e.g., electron vs. hole mobility in germanium), the charge induced by the equal number of electrons and holes generated in the interaction should be the same. The strip pairing process is further complicated by detector and electronics effects such as finite energy resolution, charge sharing between adjacent strips, multiple interactions occurring on a single strip, and energy distortion due to charge loss, including sub-threshold energy deposits (see [19] for more details). A strippairing algorithm which accommodates these effects is of the utmost importance, as accurate position determination is critical to proper event reconstruction.

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5.5 Depth Calibration Strip pairing defines the two-dimensional position of an interaction as the intersection of orthogonal strips on opposite sides of the HPGe detectors. The third dimension, depth in the detector, is derived from the collection time difference (CTD, denoted below by .τ ) of electrons and holes generated in the interaction. When a charge cloud is generated in a detector, electrons and holes drift in opposite directions along field lines to the AC and DC sides of the detector, respectively. The drift times differ depending on the interaction location. For example, the electron collection time will be less than that of the hole if the charge cloud is produced closer to the AC side. Hence, the CTD is a proxy for localizing the depth of the interaction. Each of the “pixels” (37 strips .× 37 strips .× 12 detectors = 16,428 regions segmented by the grid of orthogonal strips) in the detectors is uniquely calibrated to account for individual strip readout and variations in drift velocities across the detector volume. The calibration procedure was developed by the Nuclear Compton Telescope [27] and was subsequently implemented by COSI. A detailed explanation of the approach is provided in [28, 29] and is adapted here for brevity. Numerical simulations solve Poisson’s equation for the electrostatic potential inside a simplified .5 × 5 strip detector with appropriate boundary conditions (detector bias) and detector characteristics (impurity concentrations and thickness). The applied high voltage bias in COSI’s detectors is 1000–1500 V. The weighting field [6] is calculated by setting each strip to 1 V and rest to 0 V. The ShockleyRamo theorem [30] then uses the weighting field to calculate the current induced on the electrodes by charge carriers which move along the previously determined electric field. These simulations create a look-up table relating the CTD (.τsim ) to depth in each detector. A real CTD (.τmeas ) in each pixel of the instrument is recorded using a .137 Cs calibration source. This calibration run is then mimicked in simulations to produce a histogram of interaction depths, i.e. a simulated depth distribution, for each detector. These simulated depth distributions are converted to simulated CTD distributions from units of centimeters to nanoseconds using look-up tables. This simulated CTD distribution for each detector, called a “CTD template,” is then used to calibrate the detectors’ constituent pixels. We fit for the “stretching” .λ and “offset” . factors that most closely transform measured CTDs from each pixel into the CTD template of the detector which hosts the pixel of interest. The transformation is given by τmeas = λτsim + .

.

(4)

The .λ and . returned for each pixel are used to calculate a per-pixel .τsim that is converted to a depth via the simulated look-up table. Thus, a pixel-specific depth calibration relating the CTD and z-coordinate of each interaction is obtained.

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6 Instrument Performance In order to assess the instrument’s performance as a spectrometer, imager, and polarimeter, it is necessary to quantify the expected performance with metrics including energy resolution, angular resolution, effective area, and polarization sensitivity. This process is called “benchmarking.” These metrics are dependent on the fidelity of the previously described calibrations, and in turn on the HPGe detectors. The benchmarking results in this section (see footnote 1) are presented as a cumulative manifestation of the high-performing instrumentation and scientific achievements made possible only through the development of HPGe detector technology. Note that the data used in these analyses are fully reconstructed Compton events: the energy calibration converts ADC to energy, the temperature and cross-talk corrections are applied, the strip-pairing algorithm determines the most likely x– y positions of the interactions, and the depth calibration returns the z-coordinate of the interactions. These calibrated strip hits are then grouped as single gamma-ray events that scatter through the instrument.

6.1 Energy Resolution We study the energy resolution of fully reconstructed Compton events to understand the instrument’s spectral performance. Recall that this energy resolution differs from the single-strip energy resolution discussed in Sect. 5.1, the latter of which considers hits on individual strips. The single-strip resolution is more a measure of an individual detector’s spectral performance while the resolution of fully reconstructed events informs the spectral performance of the instrument as a whole. The energy resolution is again defined as the ratio of a reconstructed photopeak’s FWHM to its true line energy. The energy resolution as a function of energy in 2020 calibration data is shown in Table 1. COSI’s HPGe detectors have an average energy resolution of 0.7% across its energy range, granting the discriminating resolution required for high precision spectroscopic analyses.

Table 1 Fully-reconstructed energy resolution, angular resolution, and effective area in 2020 calibration data. Listed values are from [20] Isotope 22 . Na 137 Cs . 60 . Co 22 . Na 60 . Co

Line energy [keV] 511.0 661.7 1173.2 1274.5 1332.5

FWHM [keV] .5.78 ± 0.01 .5.27 ± 0.01 .6.80 ± 0.02 .7.04 ± 0.03 .6.97 ± 0.02

Energy resolution [%] 1.1 0.8 0.6 0.6 0.5

Angular resolution [.◦ ] .5.97 ± 0.04 .5.1 ± 0.1 .4.13 ± 0.04 .6.1 ± 0.3 .4.2 ± 0.1

Effective area [cm.2 ] .12.0 ± 0.5 . 9.6 ± 0.4 . 6.4 ± 0.3 . 6.1 ± 0.3 . 5.3 ± 0.2

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6.2 Angular Resolution Event reconstruction in a Compton telescope localizes the origin of an incident photon to an “event circle” on the sky. The overlap of circles from many events marks the measured location of the source (Sect. 3, Fig. 3). Ideally, in the case of a known source, this overlap lies at source’s true location. A histogram of the smallest angular distance between the source’s true location and the event circle of each event has a centroid of approximately zero. This near-zero deviation between the measured location and the true location indicates accurate localization. The fullwidth half maximum of this histogram, which represents the spread in deviation between measured and true source location, defines the angular resolution of the telescope. The angular resolution is governed primarily by the uncertainty in the 3D position of each interaction, which in COSI is dominated by the 2 mm distance between the centers of adjacent strip electrodes. The angular resolution as a function of gamma-ray energy for 2020 calibration measurements is shown in Table 1. The observed improvement in angular resolution (monotonically decreasing values) with increasing energy is expected. Incident photons of higher energy travel greater distances between subsequent Compton interactions. This increased distance between interactions improves the quality of the event reconstruction because the positions are more easily resolved. Thus, physical considerations of the interactions inside the detectors inform overall trends of angular resolution. Narrow strips spaced closer together may in theory be able to achieve improved angular resolution. However, decreasing the strip pitch increases the likelihood of a competing complication called charge sharing. Charge sharing occurs when the charge cloud of liberated electrons and holes in an interaction falls on multiple adjacent strip electrodes. Determining the position of the interaction in the detector becomes more complicated in this case. The upcoming iteration of COSI as a satellite will have a slightly finer strip pitch of 1.16 mm and is expected to improve upon the COSI’s balloon’s angular resolution by approximately a factor of two [18]. Identifying the ideal strip pitch is dependent on the specific goals and requirements of a given experiment.

6.3 Effective Area The effective area is a measure of an instrument’s detection efficiency and geometrical size. In Compton telescopes, the effective area is maximized by using a large collecting area and detector volume which can fully contain an incident photon’s multiple Compton scatters and final photoelectric absorption. For this reason, large volume HPGe detectors, like COSI’s .2 × 2 × 3 array of .8 × 8 × 1.5 cm.3 detectors (Fig. 4), are a natural choice for Compton telescopes. We scale COSI’s collecting area by an efficiency to quantify its effective area. The efficiency is defined as the ratio of the measured luminosity, or count rate, to the

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incident luminosity of radioactive calibration sources. The former is determined as the number of events in a measured photopeak divided by a known observation time. The latter is determined from the source activity and distance of the source from the instrument. Additional effects including electronic dead time and attenuation in air of incident photons are considered. Table 1 lists the effective area as a function of incident photon energy in 2020 calibration data. The radioactive sources in these calibrations were placed directly overhead the COSI cryostat at zenith; insufficient calibration time prohibited a more comprehensive study spanning the entire field of view. We observe the expected trend of decreasing effective area with increasing energy. As incident photon energy increases, so does the probability that a scattered photon escapes the detector volume before photoabsorption. Such incompletely absorbed events cannot be reconstructed and are vetoed from the analysis. The COSI satellite mission’s .2 × 2 × 4 array of 16 HPGe detectors will more fully contain the scattering path of higher energy photons and therefore have a greater effective area than the 12-detector balloon instrument.

6.4 Polarization Response Germanium’s ability to induce Compton scattering directly facilitates studies of photon polarization. Compton telescopes preserve information from linearly polarized photons via the Klein-Nishina equation (Eq. 3), which defines the crosssection of the Compton scattering process. It dictates that photons are preferentially scattered in the direction perpendicular to the incoming photon plane. Thus, photons in a highly polarized beam of light likely scatter in the same azimuthal direction (visualized by .η in the left panel of Fig. 3). The polarization angle and level are inferred from the characteristic sinusoidal shape of measured azimuthal scattering angle distributions (ASADs; Fig. 9). Higher ASAD amplitudes indicate highly polarized light. The full method of calibrating COSI and extracting the polarization information from ASADs is detailed in Sect. 7.3 and [9, 20, 29]. COSI’s unique ability to study photon polarization with its HPGe detectors provides an additional probe of the geometry and emission mechanisms of high energy sources in the gamma-ray sky, including pulsars, active galactic nuclei, and gamma-ray bursts (GRBs).

7 Scientific Achievements Launched on May 17, 2016, from Wanaka, New Zealand, COSI was the first science payload to fly on NASA’s superpressure balloon technology and remained afloat for 46 days before terminating safely over Peru on July 2, 2016. A complete overview of the flight is provided in [31]. This section (see footnote 1) summarizes the spectroscopic, imaging, and polarization achievements of the 2016 flight and,

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by extension, demonstrates the importance of HPGe detectors to MeV gammaray astrophysics. Namely, COSI observed the strong positron-electron annihilation signature at the center of the Milky Way Galaxy [32, 33], measured Galactic 26 . Al [34], detected the Crab pulsar [26], and set a constraining upper limit on the polarization of GRB 160530A [29, 35]. The upcoming COSI satellite draws significant heritage from the balloon mission as a HPGe instrument with improved sensitivity that can deepen understanding of the MeV gamma-ray sky.

7.1 Positron-Electron Annihilation A balloon-borne astrophysics mission in the 1970s discovered strong, persistent 511 keV emission emananting from the center of the Milky Way Galaxy [36, 37]. After decades of study, the dichotomy between its extended “disk” emission along the Galactic Plane and stronger “bulge” emission around the Galactic Center is not understood, nor is the primary source (or collection of sources) of the positrons fueling this annihilation. Furthermore, it is unknown whether the annihilation occurs at the sites of positron production or if the positrons propagate away from their production sites before annihilating, thereby displacing the observed emission from the positron sources. High-resolution spectroscopy of Doppler shifts in the 511 keV spectrum can probe the kinematics of and conditions in which the positrons annihilate. COSI’s balloon flight in 2016 built upon SPI’s high-resolution 511 keV spectral analyses with HPGe [38–42]. COSI detected the 511 keV line with 7.2.σ significance (Fig. 7; [3, 32]) and found a flux of (.3.9 ± 0.4) × 10−3 ph cm.−2 s .−1 , which exceeds that from SPI of (.2.74 ± 0.03) × 10−3 ph cm.−2 s .−1 [41].

Fig. 7 Observations of positron-electron annihilation in the Milky Way Galaxy from the COSI 2016 balloon flight. Left: Spectrum of the emission. The centroid of the fitted Gaussian is .511.8 ± 0.3 keV and the inherent width, subtracting out finite instrumental resolution, is .σ = 1.7 ± 0.4 keV [3, 32]. Right: Image of the emission [33] from a Richardson-Lucy deconvolution technique [43, 44]

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To complement spectroscopic studies, SPI [45–47] and COSI (Fig. 7) have also imaged the 511 keV  emission. The COSI image reveals a central 511 keV bulge  ◦ [33] that is 2–3 times larger than that reported by SPI (FWHM FWHM 28.+19 . −12 8.◦ ) [48]. It is possible that COSI measured a greater overall flux and a broader bulge than SPI because CCTs are more sensitive to small flux gradients than are codedmask telescopes, highlighting again the importance of Compton scattering in HPGe instrumentation. Improved sensitivity and angular resolution in the upgrade of COSI as a satellite mission may clarify the discrepancy between the SPI and COSI balloon results and help reveal the true nature of positron annihilation in the Milky Way.

7.2 Radioactivity and Galactic 26 Al Products of stellar and explosive nucleosynthesis decay primarily into the MeV bandpass. Studying the energy spectra of the emitted gamma-ray lines with HPGe detectors can reveal the origins and dynamics of these radioisotopes in the Milky Way Galaxy. There are four main isotopes which COSI targets for studies of nucleosynthesis: .26 Al (1.809 MeV), .60 Fe (1.173 MeV and 1.332 MeV), .44 Ti (1.157 MeV and 68 keV and 79 keV lines in the hard X-ray range), and .56 Co (0.847 MeV and 1.238 MeV). This section focuses on .26 Al, which traces nucleosynthesis in massive stars and core-collapse supernovae over its lifetime of approximately .106 years. The HEAO-3 satellite, a germanium detector, first detected .26 Al in the Milky Way Galaxy in the 1980s [49]. In the 1990s, COMPTEL produced the first images of .26 Al emission in the Milky Way [50]. Note that the energy resolution of COMPTEL’s cesium iodide (CsI) scintillator detectors was nearly two orders of magnitude worse than that of germanium and insufficient for spectroscopic studies. By contrast, SPI has conducted detailed spectroscopic studies with its HPGe detectors [51–53], detected the 1.809 MeV line with 58.σ significance [54], and produced an image largely consistent with that of COMPTEL [55]. Analysis of the COSI 2016 balloon flight data yielded a 3.7.σ significance measurement of Galactic .26 Al with an Inner Galaxy flux of .(8.6 ± 2.5) × 10−4 ph cm.−2 s .−1 [34]. This flux exceeds that reported by SPI and COMPTEL (.∼ 3.3 × 10−4 ph cm.−2 s .−1 ) by approximately 2.σ . The COSI satellite’s sixteen HPGe detectors will have the discriminating energy resolution required for detailed spectroscopic studies and decrease the likelihood that 1.809 MeV photons at the upper end of COSI’s energy range scatter out of the instrument before they are fully absorbed, thereby increasing the effective area. The satellite’s finer strip pitch will also improve the angular resolution from .∼4.◦ in the balloon to .∼1.5.◦ FWHM at 1.8 MeV [18]. This will be critical to advancing studies of .26 Al emission across the Milky Way Galaxy.

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7.3 Polarization In order to determine COSI’s polarization response and to identify systematic deviations from an ideal sinusoidal modulation, it is necessary to evaluate COSI’s polarization performance in the laboratory. This evaluation requires measuring a polarized beam and simulating the experimental configuration. We are able to produce a partially polarized gamma-ray beam using a principle detailed in [56]. When unpolarized photons Compton scatter, the outgoing beam is partially polarized with a polarization level given by =

.

sin2 φ

+ −1 − sin2 φ

,

(5)

in which . is the ratio of scattered photon energy to initial photon energy and .φ is the Compton scattering angle. The polarization vector of the scattered beam is perpendicular to the scattering plane. We produce partially polarized gamma-ray beams in the laboratory by scattering photons from a NaI scintillator. As an example, 661.7 keV photons that scatter off the scintillator at 90.◦ (to obtain the highest polarization level possible) produce a beam with an outgoing photon energy of 288 keV and a polarization level of approximately .∼58%. Using an active detector as a scattering surface allows us to select only events coincident between COSI and the NaI and thus reject the majority of the background. Figure 8 shows the geometrical configuration for pre-flight calibrations. We suspend the NaI scintillator above the instrument (GeDs within the cryostat surrounded by the CsI shields) and fix a .137 Cs source (661.7 keV) at the cryostat’s level. We place a lead brick between the .137 Cs source and the COSI detector system in order to prevent the direct flux from unnecessarily elevating the shield count rate. Acquiring data with the NaI scintillator in many different locations captures a range of polarization and scattering angles.

Fig. 8 Left: To produce a partially polarized beam, gamma-rays from a .137 Cs source scatter off of a scintillator towards the HPGe detector. Right: The setup at Space Sciences Laboratory, Berkeley, 2019. Images are from [9]

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Fig. 9 The geometrically-corrected ASAD fit with a modulation curve, the parameters of which reflect the beam’s polarization level and angle

The coincident events, which are effectively background-subtracted by calculating the number of expected chance coincidences, are used to produce a geometrically-corrected ASAD. The characteristic sinusoidal shape of a fitted, geometrically-corrected ASAD is shown in Fig. 9. The sinusoidal fit parameters correlate to the known direction of the partially-polarized beam and its induced polarization level, which is determined by Eq. 5. To effectively benchmark the simulated instrument response with calibrations, we employ non-parametric statistical tests. The Kolmogorov-Smirnov and Anderson-Darling tests evaluate the hypothesis that the azimuthal scattering angle samples from the measurements and simulations are drawn from the same underlying distribution [9]. This process confirms COSI’s ability to measure photon polarization by nature of Compton scattering in its HPGe detectors.

8 Conclusion Understanding the MeV gamma-ray sky has long been a pursuit complicated by measurement difficulties intrinsic to the energy range. Developing powerful instrumentation which can remedy the historical dearth of sensitivity in this “MeV gap” is of high priority. This chapter described the advantages of using highpurity germanium (HPGe) as a material particularly well-suited to measuring MeV gamma-rays as they preferentially Compton scatter through the detectors. Compact Compton telescopes (CCTs) are presented as a compelling configuration of HPGe detectors on an astrophysics platform, as demonstrated by the success of the COSI

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mission. The procedures needed to calibrate the detectors and quantify instrument performance are detailed; these procedures can be adapted to fit the needs of similar experiments. In conclusion, it is clear that utilizing leading technology is necessary to advance MeV gamma-ray astrophysics and that the implementation of HPGe in COSI is one such path forward for progress.

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Particle Measurements in Space Martin Kroupa, Jonathan Barney, August Gula, Carlos Maldonado, Thomas Campbell-Ricketts, and Stuart George

1 Introduction At the turn of the twentieth century, experimentalists measuring terrestrial radiation noticed a violation of expected phenomena. They knew that some minerals found in the soil were radioactive, but their expectation was that with increasing distance from the radioactivity in the earth’s soil, the rate of radiation detection would drop. However, in the summer of 1912, Victor Hess discovered that the radiation measured at the sea level is lower than that measured at higher altitudes. With the aid of balloons as observation platforms he ascended to 5350 meters with his electroscope and measured that radiation environment. At this altitude, he discovered that the rate of radiation interactions is over two times the rates he measured at sea level [1]. From this discovery, it was concluded that “radiation of very high penetrating power enters from above into our atmosphere.” This early work experimentally demonstrated that there is radiation outside the atmosphere which bombards the Earth constantly. However, due to the lack of sufficiently sophisticated detectors, Victor Hess’s experiment, like many others of the time, could say very little with regard to identifying the origin of this radiation. The detection devices used on these early

M. Kroupa () · J. Barney · A. Gula · C. Maldonado Los Alamos National Laboratory, Los Alamos, NM, USA e-mail: [email protected] T. Campbell-Ricketts Leidos Corporation, Houston, TX, USA Space Radiation Analysis Group, NASA, JSC, Houston, TX, USA S. George Department of Health and Human Performance, University of Houston, Houston, TX, USA Space Radiation Analysis Group, NASA, JSC, Houston, TX, USA © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_11

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investigations were incredibly basic and provided simple information such as approximate rates, confirmation of radiation hits, and occasionally particle tracks. Despite these limitations, some of the first hints to the complexity of the radiation arriving at the Earth were discovered. Early radiation detection devices included nuclear emulsions, which are types of photographic plates, that were sensitive to radiation. Once these photographic plates were exposed to radiation and developed, they were carefully inspected for particle tracks imprinted by impacting radiation [2]. Due to the microscopic scales on which these events took place, the analysis of nuclear emulsions was incredibly time consuming often requiring many hours or days to perform. Despite this hindrance, discoveries of several exotic particles were made. One of the very first discoveries using this technique was the .π -meson [3], which was made very early on in highaltitude investigations. Operation of nuclear emulsions for high altitude measurements was quite demanding. The sensitive emulsions had to be protected before the flight, carefully installed and removed from the balloon after the flight to be processed in the laboratories. Because of these technological difficulties, an all too familiar set of requirements was laid out. Like our modern Size, Weight, and Power-Cost (SWAPC) requirements, these early pioneers already understood that “The technical problem has three essential requirements: The apparatus must be light in weight, low in cost, and it must be reliable in operation” [4]. As these high-altitude and balloon experiments continued to be performed, the Geiger-Müller (GM) tube became the detector of choice for studying radiation. This device, though helpful in understanding rates, is very limited. The GM tubes are filled with a low pressure gas and rely on large voltage gradients between the central anode wire and the surrounding cylindrical cathode. When impinging radiation interacts with and ionizes the gas in GM tubes, the large voltage gradient causes the initial ionization to produce a cascade of electrons throughout the tube. As a result, a very clear event is produced. However, because of this electrical cascade, the GM tube has a significant recovery period, typically around 100 .μs. This means that after one particle traverses the volume of the detector the device is insensitive for those 100 .μs and if an other particle arrives during that insensitive period it would be missed. Because of this limitation in GM tubes, they are only sensitive to radiation rates up to a certain threshold. Above this threshold, the device will underreport the rate of radiation. It is also worth noting that GM tubes don’t provide any information about particle type and energy. This under-reporting became a particular point of interest during the early NASA missions of Explorer 1 and Explorer 3 (1958) which employed GM tubes as their mission payload. During the Explorer 1 mission, a rapid increase of the radiation rates was observed above 400 km. However, at 2000 km above South America an anomalous behavior was observed in the count rate. Occasionally, the instrument ˜ counts/sec, which was below the previously measured trends, or would report 30 zero counts over two minute intervals. This peculiar behavior led the researchers to take a spare flight unit of their instrument to an X-ray beam facility. From this study, ˜ they discovered that the GM tube would report zero counts per second after 35000

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X-rays/sec were impinged on the device. This was a result of the high radiation rate depleting the GM tube faster than it could recover, thus causing the pulses generated to be below the detection threshold of their electronics. Such high levels of radiation were perplexing, since the ground and high-altitude measurements of the time being performed in South America would have seen fluxes this high. As a result of this finding, the researchers concluded that there was a high radiation area above South America. This was the first discovery of the radiation belts surrounding the Earth and of the South Atlantic Anomaly (SAA) [5]. Today we know that the magnetic field of the Earth is able to “trap” the charged particles, which then traverse along the magnetic field lines. The Earth’s trapped radiation environment is very energetic and consists of different types of radiation, mainly protons and electrons [6–10]. These high radiation areas are called the Van Allen belts and are a primary concern for satellites. Earth has two main belts—the inner belt, typically between 1000 and 12,000 km in altitude, consists predominantly of protons with some electrons, and the outer belt consists mainly of electrons and sits between 13,000 and 60,000 km. Due to the magnetic axis of the Earth being tilted and also shifted with respect to the rotational axis, the inner belt above South America can reach altitudes of 200 km, creating the SAA. In addition to the trapped radiation population, a constant stream of Galactic Cosmic Rays (GCRs), which consist of all kinds of particles and elements from hydrogen to uranium, bombards the Earth. The energy of these GCR particles covers many orders of magnitude. We have observed particles ranging from those that can be stopped by a thin sheet of paper to the particles with macroscopic energies. The record holding “Oh-My-God” particle, which had an energy about .3 × 1020 eV, had the equivalent energy to a baseball flying at 100 km/h. This energy is about seven orders of magnitude higher than the fastest particles we can produce in the most potent particle accelerator on Earth, the Large Hadron Collider (LHC). GCR count rates are many orders of magnitude lower than the trapped ones. However, it turns out that not only the rates but also the composition of the radiation environment is important, and we will discuss it later. From radiation protection point of view, the energy of the GCR particles prevents effective radiation shielding as it is currently not possible to bring enough shielding material to space to block the GCR. The last source of the charged particles in the near Earth environment is Solar Particle Events (SPEs). These unpredictable events release a massive amount of particles (orders of magnitude higher fluxes than GCR) from the Sun and eject them into the solar system. The unpredictability and severity of such events causes a lot of sleepless nights for the individuals responsible for human space flight. Indeed, during the Apollo program, a solar storm occurred during the time between the Apollo 16 and Apollo 17 missions (August 1972). Exposure to this harsh environment while on the surface of the Moon would have caused significant risk for Apollo crews. In the case that an SPE were to have occurred, the contingency strategy while on the surface of the Moon was to lie down under the lunar module with one astronaut on top of the others and to swap positions every 10 minutes. An interesting phenomenon was also described by the Apollo 11 crew in the middle of the program, in which astronauts reported seeing flashes of light even

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Fig. 1 Landau-Vavilov distribution, which describes the probability of the energy deposition for a given particle type and energy in the material. This example represents a high-energy (minimum-ionizing) proton. The distribution is asymmetric with a tail toward high energy losses. For comparison, real measured data and a Monte-Carlo model for the corresponding detector are shown too. There is a slight difference between analytical Landau-Vavilov and Monte-Carlo results. Figure taken from [19]

when their eyes were closed. When other crews were asked, it was confirmed that every crew member observed the optical flashes. Thus from Apollo 15, the crews had dedicated time slots to investigate this phenomenon. It turned out that the flashes are a response of the human visual system to the space radiation [11, 12]. Following the Explorer missions it was recognized that the greatest need in studying this environment was the ability to separate particle populations. As mentioned previously, nuclear emulsions were used to measure and distinguish different particles, particularly those with high atomic number [13]. Additionally, this technology was quite fragile and required extensive processing at the groundbased lab. Because of this, an effort to use active detectors together with known charged particle stopping power physics [14–18] has been adopted. For charged particles penetrating matter, the energy loss inside the material is probabilistic. The probability distribution of this energy loss is highly asymmetric with a tail toward high energy losses (see Fig. 1). This asymmetry results from the fact that as a particle travels through matter, ionizing atoms along the way, it can sometimes hit an electron “just right” and give it much more than the mean amount of energy. These high-energy electrons, if stopped inside the detector volume, cause the high energy deposition tail in the Landau-Vavilov distribution. As one would imagine, if we are interested to know what the energy of an interacting charged particle was, then we would try to reconstruct the energy using several measured energy losses throughout a detector. Due to the statistical nature of the energy loss, it is significantly better to sample the energy losses of the charged particle in a

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multi-layered detector. By comparing the energy losses in these detector layers to the stopping power, a reconstruction of the energy can be derived. These multi-layered detectors, or particle telescopes, were the next level of advancement employed to understand the high energy particle populations in the radiation environments surrounding the Earth. This paradigm-shift in detection methodology allowed for the collection of both low and high energy GCR particles while efficiently separating light and heavy charged particle populations. Despite many of these early technical advancements being a part of the space race between the USSR and USA [20], some were for purely scientific purposes. Highlights leading up to the present time were the missions of the International Sun-Earth Explorer (ISEE) [21], the EXOspheric Satellite-C (EXOS-C/OHZORA) [22], the Solar Anomalous and Magnetospheric Particle Explorer (SAMPEX) [23], and the Combined Release and Radiation Effects Satellite (CRRES) [24]. The first of these missions, the ISEE missions, was one of the first examples of a long-term multi-satellite and multi-experiment missions [21]. The lessons learned from the multitude of prior Explorer missions in the 1960s and 1970s were applied to the ISEE-1, .−2, and .−3 satellites. These insights, particularly in the choice of instruments aboard, led to the variety of instruments aboard these satellites being quite diverse. Experiments ranged from electromagnetic field measurements to charged particle detectors and ion spectrometers. Though there were significant technological advancements in implementing particle telescopes, there were also drawbacks. At the time, in order to perform energy measurements over a wide range of energies, multiple solid-state detector telescopes were required [25, 26]. With such a large energy range to cover, one such telescope existed for just the low to medium energies, the Very Low Energy Telescope (VLET). This telescope itself was made up of four detectors along with its own shielding and electronics to cover only the 2–8 MeV/nucleon energy region. There were additional telescopes aboard for low, medium, and high energies [21]. For missions seeking to have low SWAP-C, this kind of specialization in devices presents a problem. Compounding the SWAP-C problem is cost: a large investment is required to produce these satellite observatories. That is why, as missions continued to be developed and technological advancements occurred, a miniaturization of electronics and technology has been a boon to space research. As technology continued to improve, the volume and mass of these payloads continued to decrease, and more compact designs were made. However, despite this miniaturization, the fundamental principle remained: a multi-layered device must be used to separate particle energies, species, and trajectories. In the case of the Small Explorer missions for low cost spacecraft, the SAMPEX spacecraft is one such beneficiary of these advancements while retaining scientific potency. Though the number of instruments aboard SAMPEX pales in comparison to ISEE, the science did not. SAMPEX lasted a year longer than ISEE-1 and the energy range of its four instruments covered an appreciable .≈0.4–.≈300 MeV/nucleon compared to the energy range .≈1–.≈500 MeV/nucleon of ISEE with its telescope instruments. Though the energy range had decreased, so did the mass of SAMPEX.

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SAMPEX measured around 158 kg, which is significantly smaller SWAP-C compared to ISEE-1 with a weight of 340 kg. With every gram to orbit having a large cost associated with it, these advances in technology miniaturization have proven to pay great dividends.

2 Challenges of Using Particle Telescopes As described above, particle telescopes effectively sample the stopping power of charged particle radiation and allow for the reconstruction of the particle’s kinetic energy. In order to perform this reconstruction, the impinging radiation typically needs to travel close to the axis through the layers of the telescope. In space, however, these particles can originate from all directions and potentially miss several of the telescope layers. A particularly frequent and troublesome case of this occurs when a high energy particle penetrates the shielding surrounding the telescope and interacts with a single layer as it passes through. For cases such as this—where a background signal is generated in an arbitrary layer—these events can overwhelm, undermine, and obfuscate the energy reconstruction process. Over many years of use and development, several different strategies have been produced to combat such issues with particle telescopes. The simplest solution is the implementation of collimation. By limiting the field of view to angles very near coaxial with the telescope, not only can lower fluxes be obtained but the low energy background can be drastically suppressed (as discussed above, background are the events which are not of interest, but still are being processed by detectors and their electronics). The use of a collimator, however, typically adds significant size and weight to a particle telescope in addition to the collimation effectiveness being limited by the energy range of interest. For particles with high kinetic energy, it is impossible to create a robust enough collimator within reasonable size and weight constraints. For example, 10 MeV protons have range of about 700 .μm inside silicon, 100 MeV protons have a range of about 40 mm, and for 1000 MeV protons it is about 1.7 m. For cases where high energy particles are of interest and collimation would become cumbersome, hardware or software solutions are often implemented. In these cases, one can require that only the events depositing energies in all telescope layers will be assessed and recorded. A recent example of such an approach was implemented on the Van Allen Probes high energy telescope named the Relativistic Proton Spectrometer (RPS) [27]. Another option in such regimes of interest is to determine if the particle entered the telescope at an angle by including an anticoincidence layer on the sides of the telescope. If a particle hits this anticoincidence detector, then the event is discarded. This was the approach used by the Radiation Assessment Detector (RAD) on the Mars Science Laboratory [28], which we know colloquially today as the Curiosity mission (although in this case the anticoincidence was used for separation of the charged particle and neutron signal).

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Fig. 2 The stopping power, or mean Linear Energy Transfer (LET), for a selection of nuclei, as a function of energy per nucleon of the projectile. These values were calculated using the Bethe formula. For H, He, and C, the spread of observed energy depositions around the mean LET is indicated at 100, 400, and 800 MeV/nuc, by overlaying the relevant Landau-Vavilov distributions. The overlap between these Landau-Vavilov curves, for example for hydrogen at 400 and 800 MeV/nuc, illustrates the difficulty in using a single LET measurement to infer particle energy

An unfortunate limitation of charged particle telescopes comes in the scientific reality that for very fast particles the stopping power does not vary significantly over a wide range of high energies. The Bethe-Bloch formula, which describes the stopping power of charged particles as a function of the particle energy, has a minimum around 2.5 GeV per nucleon (Fig. 2). Charged particles near this energy will deposit, on average, the smallest energy possible inside a detector. These particles are called Minimum Ionizing Particles, or MIPs for short. Additionally, the difference between the stopping power of a 1, 2.5, and 10 GeV particle is rather small. Because of this, it is typically impossible to assess the energy of such particles using just a sampling of the stopping power. Therefore, additional physical processes need to be taken into account if this high energy region is to be distinguished. For very fast-moving particles, such as these, the traversing particle will create light as it penetrates through a material. This light is called Cherenkov radiation and can be detected with photo-sensitive materials, allowing for additional information on these MIPs. Such considerations were implemented on the RPS, which used a Cherenkov detector in its design [27]. Alternative telescope designs have been used to measure this energy region. An extreme example is the Alpha Magnetic Spectrometer (AMS) experiment operating on the International Space State (ISS) [29]. The most recent version, AMS-2, is a several billion dollar and over 6500 kg instrument flying on the ISS [30]. This

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device utilizes strong magnetic fields to distinguish particle energies, because the bending of the trajectory of the charged particles in the magnetic field is a function of the kinetic energy via the Lorentz Force. By measuring the final position of these charged particles inside the AMS-2, very high energy particles can be distinguished from each other. There has been a growing interest in the space physics community for satellite constellations missions to enable multi-point observations capable of resolving temporal and spatial science investigations [31, 32]. This new wave of mission concepts has been fueled by the current era of rapidly expanding CubeSat launch opportunities and the increased demand for low-resource instruments capable of making relevant science observations. This interest, combined with advances in sensor and other spacecraft technologies, has enabled the rapid increase in the number of miniaturized charged particle detectors with flight heritage. The Relativistic Electron and Proton Telescope integrated little experiment (REPTile) on board the Colorado Student Space Weather Experiment (CSSWE) CubeSat mission was one of the first missions to demonstrate the ability of CubeSats and miniaturized instruments to produce high quality science returns [33]. The instrument design was based on the Van Allen Probes Relativistic Electron and Proton Telescope (REPT) [34] and consisted of four solid state detectors encased in aluminum and tungsten shielding. Similarly, the Miniaturized Electron pRoton Telescope (MERiT), a 1U device consisting of a stack of solid-state detectors behind space facing avalanche diodes, was flown in a low polar Earth orbit to investigate electron microbursts and to study solar particles [35]. Embracing the design paradigm of “faster, cheaper, better” [36] the Falcon Solid State Energetic Electron Detector (SEED) pushed the bounds of low-resource instrumentation by demonstrating the ability of a single element telescope consisting of Commercial Off The Shelf components to successfully operate in GEO for one year [37]. The SEED experiment also demonstrated the ability of a low resource charged particle telescope to provide comparable measurements to state-of-the-art payloads [38]. These modern CubeSat missions, hosting next generation miniaturize charged particle telescopes, are now targeting more ambitious missions with the promise of significant science returns. Among these are two CubeSat missions, the Geostationary transfer orbit Satellite (GTOSat) [39] and the Experiment for Space Radiation Analysis (ESRA) [40–43], that will for the first time, attempt to operate through GTO providing observations of proton and electron energy resolved rates. The ESRA mission will utilize a five-element detector stack consisting of Si detectors of varying thickness and a photodiode [44, 45]. The GTOSat will host the Relativistic Electron Magnetic Spectrometer (REMS), a miniaturized version of the MagEIS-Medium instrument onboard NASA’s Van Allen Probes to measure high energy electrons [9], and the micro Charged Particle Telescope (.μCPT) to measure energetic proton populations [46]. The GTO environment is extremely stressing and hazardous for satellites since they cross both the inner and outer Van Allen radiation belts multiple times each day. Additionally, the success and subsequent flight heritage of the first MERiT mission enabled the instrument to be manifested as a science payload on the CubeSat Mission to Study Solar Particles (CuSP) which was launched in a heliocentric Earth-escape orbit [47].

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3 Crew Dosimetry Since the early NASA days it was clear that radiation monitoring will be an important part of all crewed missions. Quantifying the impact of the radiation to the human body is a complicated subject which is even more convoluted by the fact that radiation environment in space is so different than that on the surface of the Earth. Traditionally the impact of the radiation to the body was measured using dose, which is the quantity representing the energy deposited to the mass. However, it turned out that impact of different types of radiation is different, and measuring just the dose is not enough. Hence the so called quality factors and dose equivalent were introduced. Quality factors are trying to weight the impact of different types of radiation to the body, however the weighting is coarse. To measure dose and dose equivalent different detector technologies have been used, ranging from passive Thermoluminescent dosimeters (TLDs) to Tissue Equivalent Proportional Counters (TEPCs). Progress in biomedical physics produced better understanding of the differing impacts of radiation on the human body, allowing NASA to abandon dose and dose equivalent paradigm to introduce the new Risk Assessment model [48, 49]. For this model, the fluxes of different particles are required as an input. In other words it is not enough to know how much dose was absorbed, but it is required also to discern what type of radiation is present. This in fact means that particle telescopes should be utilized. The Space Radiation Analysis Group (SRAG) at NASA Johnson Space Center (JSC), which is responsible for crew safety from mission exposure to radiation, consequently started to work on the next generation radiation monitors for their future crewed missions in the early 2010s. The requirement for the next generation radiation monitors was to be compact, but able to provide more information than traditional TLDs and TEPCs. From the explored detection technologies the pixel detector technology has been selected. In the last decade, NASA invested heavily in this technology and utilized it for radiation monitoring during crewed missions [50]. In fact, Timepix which is the detector to use became the state-of-the-art technology for radiation monitoring during crewed missions (all NASA Artemis missions are scheduled to use this technology). Twenty-three Timepix detectors have been used in seven different NASA missions in the last decade. Further utilization in four missions in the near future is also planned.

4 Pixel Detectors Recent developments in electronics have allowed for the continued significant miniaturization of devices. The development of dedicated Application-Specific Integrated Circuits (ASICs) based on Complementary Metal-Oxide Semiconductor (CMOS) technology has enabled the creation of many of these miniaturized devices. An example of these miniaturized devices are pixel arrays with dedicated Front End

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Electronics (FEE) in each pixel. A significant result of these developments is that the output of such devices can be purely digital, simplifying the data processing pipeline. An example of these pixel arrays is the Timepix detector [51], which originated from the Medipix collaboration based in CERN [52]. The Timepix device is a hybrid pixel detector. Hybrid technology allows for the separation of the read-out ASIC and the active volume sensor. These two media are bump-bonded together via flip-chip technology. The benefit of using this hybrid technology is that the sensor can be a different material to the ASIC, which allows the sensor material to be optimized for a given application. Thus, Timepix detectors have been used with a variety of sensors made of different thicknesses or materials ranging from Si, CdTe, GaAs, and even gas chambers [53–55]. Since the Timepix detector is a fully digital device, it possesses many advantages in its use. One can look at the Timepix as a digital camera for radiation, taking snapshots of the environment, referred to as frames, over adjustable frame acquisition times. Adjusting the acquisition time thus allows operation in the wide variety of environments. In each frame the interacting particles create electron-hole pairs in the active detector volume. These are collected by an applied bias voltage and processed by the read-out ASIC. Only signals above a certain energy threshold in the pixel are processed and digitized, allowing for the elimination of dark current from the device. Because of this, the detector can be operated for “infinite” time and the counters will be increased only when the radiation hits the pixel volume. This makes the usage of these detectors for particle detection very easy as there is no need of any background subtraction. If those pixel detectors are used for X-ray imaging , this allows for a continuously improving signal to noise ratio. As a result of this advantage, Timepix detectors are widely used in micro-tomography applications and for exploring new imaging modalities such as phase contrast imaging [56]. There are several different modes that each pixel can be operated in. The most basic one is the counting mode, in which the device counts how many particles were above the threshold during the acquisition. As the digital shutter opens, the counters in each pixel are increased when the signal crosses the pixel threshold. This mode is typically used for imaging, there is no energy information in this mode.1 The most common mode for space applications is Time Over Threshold (TOT). This mode allows for the measurement of the length of the signal above the threshold. As soon as the signal crosses the threshold the pixel counter starts adding clock ticks until the signal crosses below threshold. Timepix can operate at different internal clocks, but typically the 10 MHz clock is used. The set of internal Digital to Analog Converters (DACs) allows optimizing the analogue circuit shaping [57]. The length of the analogue signal can be thousands of clocks or hundreds of microseconds. It can be shown that this length is proportional to the energy deposited. Timepix, therefore, with its .256 × 256 pixel array, provides measurements from over sixtyfive thousand multichannel analyzers simultaneously [58]. However, in order to

1 With

exception on the low energy limit given by the threshold.

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have good measurements, at most one particle should hit each pixel during the acquisition time, as the signal from all particles will be summed when the shutter is opened. Operating Timepix detectors in space thus requires automatic adjustment of the length of the measurement, where the occupation of the detector matrix is evaluated, and the shutter time is adjusted accordingly. To avoid overlap of clusters we typically aim at the maximum occupancy (active pixels) of 2%. On ISS, frames with acquisition time of 4 s typically have much less than 2% occupancy. However, when the ISS crosses the SAA the acquisition time has to be shortened in order to keep occupancy low. Thus, during the SAA crossing the acquisition time typically settles around a couple hundred milliseconds. When on Orion vehicle and crossing the Van Allen belt, acquisition times of millisecond length were observed. The shortest acquisition time which still provides reliable data is in fact in the milliseconds. If the acquisition time would be shorter there is a high chance that the signal from particle would be clipped by the end of the shutter window and energy measurement would not be correct. Originally these detectors were designed for X-ray imaging with their FEE being optimized for energy depositions in tens of keV. Significant efforts were made recently to push the calibration of these devices into the MeV range [19]. From these efforts, it was discovered that this task is not as simple as first envisioned. The electronics are overwhelmed by the large signals originating from charge particles and the preamplifiers are saturated by this signal. As the signal returns from this saturation, an extra fake signal is produced and causes the energy calibration to be non-linear. The so-called “advanced calibration method” was invented and allowed for compensation of this fake signal [19]. This method allowed for the calibration to be extended up to about 2 MeV. For higher energy depositions the signal is affected by the so-called “volcano effect” where a portion of the signal is lost due to the saturation time being longer than the measuring time [59]. Such high energy depositions almost invariably lead to signals in neighboring pixels, the analysis of which was shown to allow the total deposited energy to be reconstructed and the calibration extended up to 8 MeV per pixel. Because of this, the Timepix detector can be used for cosmic ray particles up to iron and thus enables the practical measurement of all particle species of interest to NASA crewed missions.

4.1 Pixel Data Analysis Because of the highly pixelated nature of Timepix detectors, they can provide significant advantages in charged particle measurements. Specifically, the Timepix detector mimics a Wilson cloud chamber in solid state, allowing for analysis of the tracks of interacting charged particles. Common use of Timepix detectors led to development of a data analysis toolkit by NASA which allows for the identification of all independent particle tracks in the detector. We will call these analyzed tracks “clusters” in this chapter. Using image processing techniques, several properties of each cluster can be identified,

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such as the entry angle. Combining this with the known thickness of the sensor and the assumption that the particle fully penetrated the sensor, one can estimate the particle track length inside the detector [60]. Using this information, together with the measurement of the energy deposition, one can then assess the energy lost per unit length or dE/dx. This measurement is crucial for particle identification and energy reconstruction. A first demonstration mission of the commercially available instruments based on the Timepix detector started in 2012 when 5 Radiation Environment Monitors (REMs) were deployed to the International Space Station (ISS). This was highly successful and showed viability of these detectors for the desired purpose. In the next ten years Timepix based detectors were part of 7 missions with a total of 23 detectors being deployed. At the same time NASA started developing its own devices using Timepix detectors. This effort resulted in the Hybrid Electronic Radiation Assessor (HERA) which is the radiation monitor for the NASA Orion vehicle and recently flew aboard of the Artemis I mission around the Moon. Because the data these detectors provide can yield such crucial information, Timepix based devices can provide a wealth of highly valuable scientific results as well as interesting surprises. During the inaugural NASA Orion vehicle flight, called EFT-1, the Battery-operated Independent Radiation Detector (BIRD) was the only scientific payload on board. This payload was based on Timepix technology. During the highly eccentric trajectory of EFT-1, two crossings of the Van-Allen belts occurred. When the BIRD data were analyzed, it was discovered that during parts of the trajectory there was a large increase in low energy photons with a specific energy of 25 keV. Following further investigations, those photons were shown to be a tertiary effect of detection. While Orion crossed the electron belts, significant Bremsstrahlung was created in the walls of the vehicle. Bremsstrahlung photons irradiated the Timepix detector and hit the bump-bonds. These bump-bonds are made of tin, which has an X-ray fluorescence line of 25.27 keV. It was later shown that a similar signal is measured on the ISS as well, and undergoes enhancement as geomagnetic storms occur. In a very unexpected way, it was shown that a detector inside the crew vehicle can provide information about outside environment which is unable to penetrate the vehicle’s walls. Another interesting discovery was the recording of pion showers [61]. Some frames from ISS showed very significant events with thousands of particles in one frame and basically none in the one before and after the event (see Fig. 3). This means that the event was very narrow in time. The clusters in the frame also showed directional correlation, looking like jet events from high energy physics. It is assumed that these events are the result of interactions between very high energy particles (often in excess of 1 TeV) and the mass of the ISS or detector, creating hadronic showers. These events are so potent that up to 1 GeV can be deposited inside the volume of the detector. The observation opens the question about the impact of these super high energy events to the field of dosimetry. The main concept of dosimetry is that the dose deposited in the detector and body would be the same. However in the case of showers which develop in the matter this requirement might not be satisfied. In other words, the shower, while traveling through human body,

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Fig. 3 Time evolution of a typical shower event. The observed temporal pattern, together with the highly aligned nature of the tracks confirm this as a shower event, originating at a single point somewhere in the vehicle. (a) Frame before the event. (b) Frame of the event. (c) Frame after the event

would evolve more, creating more particles and depositing more energy than it would in the smaller volume of the detector. The extreme situation would be when the shower is started inside the human body, thus the measured dose from radiation monitor and dose deposited to the human body would be completely uncorrelated.

4.2 Single Layer Particle Telescope NASA’s experience with Timepix for particle spectroscopy, as part of its spacebased dosimetry effort, has led to a realization that an array of pixels represents a generalization of the particle telescope concept, both extended to two dimensions, and achieved in highly miniaturized form. Thus, noting the 55 .μm pixel pitch characteristic of the Timepix, a penetrating particle incident, for example, at 60.◦ to the surface normal of a 500 .μm thick sensor will traverse almost 20 pixels, each of which can be considered a virtual telescope layer. For this reason, we will sometimes refer to our pixel detectors as single layer particle telescopes. [62] The advantage of this approach is not only the size of the whole detector, but also the fact that whole energy deposition is known and recorded. There are no insensitive material or dead layers in between telescope layers as the layers are just virtual parts of the same pixelated silicon. As noted, particle telescopes were devised to overcome the highly stochastic mapping from kinetic energy to dE/dx. By taking several samples of the latter, a better estimate of the former can be obtained. For many spectroscopic applications involving pixel detectors, the amounts of energy deposited in each pixel along a particle track can be considered to be very nearly independent, in which case this desire for multiple dE/dx samples is easily met. A maximum-likelihood approach, making use of this multi-pixel information has been demonstrated to give significantly better kinetic energy reconstruction than simply using a single dE/dx

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measurement for the whole cluster [62]. The longer the cluster is, the more pixels are involved, and more virtual telescope layers can be used. If the particle entry angle to the sensor volume is the normal to the surface of the sensor, the sampling is not possible, and we obtain just one virtual telescope layer. For good performance of the method an entry angle of the particle larger than 60.◦ with respect to the normal of the surface is desirable. The field of view of such telescope is then a donut-shaped structure, opposite to the typical cone field of view known from regular telescopes. Thanks to pixelization, the Timepix detector can be used to reconstruct kinetic energy of the particles in relatively broad range. Data published in [62] showed very good reconstruction capability up to 400 MeV protons. For higher energies, the energy resolution of the device and the characteristic of the energy loss are a limiting factor, but it was shown that these data can be still used for a good integral measurement. This approach applies broadly for different particle species and thus not only energy but also particle type can be evaluated. The method was tested on the protons, alpha particles, CNO group and high Z (iron like) particles. The single layer telescope concept also offers great utility in cases where dE/dx is varying systematically along the track, i.e. when a particle slows down appreciably within the detector. In such cases, it has been found that rather than needing to examine each pixel individually, much of the information content is captured in the energy deposited at either end of a long track. The high resolution of this technique, relative to other telescope devices, stems from the high pixel density in the Timepix, coupled with our ability to select subcluster elements larger than the individual pixel. From geometric analysis of the pixel pattern in a cluster, we have an excellent estimate of the track angle, making it possible with long tracks to select just the right number of pixels in each subcluster to provide a uniform subcluster length. This contrasts with many other particle telescopes, where the path length in each detector element varies over the opening angle of the device, and one is forced to apply some mean chord length in order to go from .E to dE/dx. The strength of this method was highlighted when the analysis of Timepix data from ISS allowed identification of the proton isotopes with resolution unprecedented for a device of this compactness [63]. In this work we focused on stopping particles, i.e. particles that do not penetrate fully the detector volume. When a particle slows downs and stops in the detector it deposits more energy per unit length at the end of its track. This terminal spike in deposited energy is called the Bragg peak and is always the same for the given particle type [18]. Segmenting a cluster to provide two parts of fixed length at the beginning and end of the track, one can search for these tell-tale Bragg energies. When any of these energies is found, one can confidently identify the particle species. Thus, we were able to discriminate different isotopes of hydrogen, namely protons, deuterons, and tritons. Results from [63] are summarized in the Fig. 4. Different areas in the Fig. 4 can be discussed. Areas on the .dE/dx1 = dE/dx2 line corresponds to the particles where the stopping power didn’t change dramatically while going through the material of the sensor. Namely Area A corresponds to minimum ionizing particle (MIP) of protons. We can observe broadening

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Fig. 4 dE/dx vs dE/dx plot from single Timepix device. Data taken onboard the ISS, figure taken from [63]

about the line .dE/dx1 = dE/dx2 which is caused by statistical fluctuations in energy deposition for penetrating charged particles as discussed above (see Fig. 1). Similarly Area B corresponds mainly to MIP helium ions (there would be a contamination of the slow protons which have same stopping power as fast helium ions). Slowing down of the particles can be seen in Area C where two branches diverge from the .dE/dx1 = dE/dx2 line. Areas D, E, F, and G are including particles which significantly slowed down in the sensor material and are stopping inside the detector. It was shown that these areas correspond to different isotopes of hydrogen (Areas D, E, F are for protons, deuterons and tritons respectively) and helium (Area G). Observation of features corresponding to three hydrogen isotopes in a single layer is the result of a level of track-length resolution not possible with a single, monolithic sensor of the type used in traditional particle telescopes. This ability to identify stopping particles using subcluster analysis also improves the measurement of linear energy transfer (LET), which is a common quantity measured for particles. With monolithic detector elements, in order to measure LET, one is typically forced to assume that the particle penetrates the whole detector volume, in order to calculate .x. For stopping particles, this assumption is clearly violated, and the path length within the sensor is uncertain. Utilizing whole-cluster LET analysis

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with a 300 .μm thick sensor on a Timepix, for example, it was shown that stopping particles create an artificial peak at around 10 .keV /μm in the LET spectrum [64]. By identifying stoppers and removing them from the LET spectra it was shown that the LET peaks from minimum ionizing ions of the CNO (Carbon, Nitrogen, Oxygen) group can be resolved [63].

5 Summary The journey for the development of the smallest possible particle detectors took a fast pace over last decade. As shown by the success of the Timepix detector technology, miniaturized devices the size of an index finger can provide rich quantitative and qualitative information. The importance of this technology was recently highlighted, with the HERA radiation monitors aboard of the Orion vehicle flying around the Moon.2 The future of space exploration is bright and exciting. The push for new technologies will continue, and we eagerly anticipate learning what the next chapter in space radiation measurements will bring.

References 1. Angelo, J. (2004). Nuclear Technology (Sourcebooks in modern technology). Westport: Greenwood Press. ISBN: 9781573563369. https://books.google.com/books?id=ITfaP-xY3LsC. 2. Walter, M., & Wolfendale, A. W. (2012). Early history of cosmic particle physics. The European Physical Journal H, 37(3), 323–358. 3. Lattes, C. M. G., Muirhead, H., Occhialini, G. P. S., & Powell, C. F. (1947). Processes involving charged mesons. Nature, 159(4047), 694–697. ISSN: 1476–4687. https://doi.org/10. 1038/159694a0 4. Johnson, T. H. (1937). Radio balloon-measurements of the cosmic radiation. Eos, Transactions American Geophysical Union, 18(1), 150–151. https://doi.org/10.1029/TR018i001p00150-2. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/TR018i001p00150-2 5. Van Allen, J. A., Ludwig, G. H., Ray, E. C., & McIlwain, C. E. (1958). Observation of high intensity radiation by satellites 1958 alpha and gamma. Journal of Jet Propulsion, 28(9), 588– 592. https://doi.org/10.2514/8.7396 6. Rossi, B. (1964). Cosmic rays. New York: McGraw-Hill. 7. Badhwar, G. & O’Neill, P. (1996). Galactic cosmic radiation model and its applications. Advances in Space Research, 17(2), 7–17. Proceedings of the Meetings F2.6 and F2.7 of COSPAR Scientific Commission F which was held during the Thirtieth COSPAR Scientific Assembly. ISSN: 0273-1177. http://dx.doi.org/10.1016/0273-1177(95)00507-B. http://www. sciencedirect.com/science/article/pii/027311779500507B 8. Bourdarie, S., & Xapsos, M. (2008). The near-earth space radiation environment. IEEE Transactions on Nuclear Science, 55(4), 1810–1832. ISSN: 0018-9499. https://doi.org/10.1109/ TNS.2008.2001409

2 On

Artemis I mission November 2022.

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Photon Counting Detectors: Applications in Radiotherapy Alex Winkler

Following abbreviations are used in this chapter. Ag b B Be BNC BNCT CBCT Cd CdNC CdTe CdZnTe CMOS Co Cr Cs CT eV EID ERBT F Ge Gy HPLC Hf

Silver Barn, unit of nuclear cross sections Boron Neutron Capture Beryllium Boron Neutron Capture Boron Neutron Capture Therapy Cone Beam Computed Tomography Cadmium Cadmium Neutron Capture Cadmium Telluride Cadmium Zinc Telluride Complementary Metal Oxide Semiconductor Cobalt Chromium Caesium Computed Tomography electron Volt Energy Intergrating Detector External Radiation Beam Therapy Fluorine Germanium Gray, unit of absorbed dose of ionizing radiation High Performance Liquid Chromatography Hafnium

A. Winkler () Helsinki Institute of Physics, University of Helsinki, Helsinki, Finland e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 C. Hansson, K. (Kris) Iniewski (eds.), X-ray Photon Processing Detectors, https://doi.org/10.1007/978-3-031-35241-6_12

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Hz Ir IRT IORT LET Li Linacs Mn MRI NCT O PC Pd PCD PET PG RT Si SNR SOBP SPECT Ta Te W Zn

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Hertz, unit of frequency Iridium Internal Radiation Therapy Intraoperative Radiation Therapy Linear Energy Transfer Lithium Linear accelerators Manganese Magnetic Resonance (tomography) Imaging Neutron Capture Therapy Oxygen Photon Counting Palladium Photon Counting Detector Positron Emission Tomography Prompt Gamma Radiation Therapy Silicon Signal to Noise Ratio Spread-Out Bragg Peak Single-Photon Emission Computed Tomography Tantalum Tellurium Tungsten Zinc

1 Radiotherapy Introduction Radiation therapy (RT), also known as radiotherapy, is a form of cancer treatment that utilizes high-energy radiation. The goal of RT is to deliver a lethal dose of radiation to the tumor (cancer stem cells), while minimizing exposure to healthy tissue. The treatment may be realized as the primary therapy for treatment, or used in conjunction with surgery, chemo, or other therapies. Typical RTs are divided into daily sessions that are distributed over a period of several weeks until the prescribed does is reached. The radiation provided for RT can be delivered externally using specialized accelerators, or internally, through the placement of small radioactive sources inside the body. The detection of the radiation is an essential part of RT and has been an element therapy’s development since its introduction. However, the requirements to detectors used for RT show several principal differences compared to diagnostic imaging applications. Radiation hardness and signal intensity are two of the most pronounced

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differences. These lead to several additional difficulties for the adoption of photon counting detectors (PCDs) in RT which are discussed in this chapter.

1.1 History Conrad Wilhelm Röntgen’s discovery of the X-rays in 1895 lead quickly to the application in medical imaging, with the first X-ray images being acquired for surgical applications within a year from their discovery. It is less known that the first breast cancer patient was also treated within one year from the discovery of X-rays [15]. Although with questionable success, as the adverse effects of ionizing radiation were only begun to be collected a few years after Röntgen’s initial discovery. As practitioners and patients found to experience inflammations, blistering, ulceration and necrosis at the areas of exposure to X-rays. This quickly lead to more dedicated and sophisticated trials of treating various skin and superficial carcinomas with X-rays. Whilst deeper laying tumors required ionizing radiation with larger energies in the range of MeV. These became widely available after the invention of nuclear reactor and their possibility to transmute stable elements to radioactive isotopes through neutron bombardment [12]. H.E. Johns presented in 1949 the first prototype that employed .60 Co as source for higher energy ionizing radiation, in order to treat deeper seeded tumors. He developed the concept quickly further and his proposed Cobalt-60 Units established as the main source for radiation therapy until the 1970s. At that time the development of linear accelerators (Linacs) made sufficient advances to provide beams with high enough energy, intensity and operation time to replace the established Cobalt Units. Since then numerous generations of medical accelerators have been iterated and are nowadays the main tool for contemporary radiation therapy. Larger hospitals often operate 10s of linacs to serve their districts. These comparably cheap devices deliver electron or X-ray beams, whiles further specialized accelerator types have been developed for other radiation therapies such as proton, carbon or neutron therapy. Linacs accelerate particles through the use of an oscillating electrical potential. Whereas the frequency of the oscillation being in historically in the MHz and thus radio frequency region. For X-ray Linacs, electrons are accelerated to 20 MeV or more and are directed on suitable target materials such as W. This results in Xray energies up to the acceleration voltage of the electrons. The overall principle is similar to that of an X-ray tube, however with substantially higher spectral energies. Modern Linacs are equipped with a low and high energy imaging system referred to as kV and MV imager. These are discussed in Sects. 2 and 4. An example of an X-ray Linac is presented in Fig. 1. Except for neutron therapy, are dedicated Linacs for particle therapies focusing the beam directly on the patient, hence do not require a target material. This necessitate additional beam focusing elements and substantially larger acceleration electronics, due to the higher mass of protons and ions compared to electrons. Linacs

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Fig. 1 An X-ray Linac for radiation therapy at the Oulu University Hospital, Finland. The devices on the arms are an X-ray tube and corresponding detector, as well as the Portal imager retracted on the bottom. Credit to Dr. Mikael Brix, Dr. Sakari Karhula, Oulun Yliopistollinen Sairaala—OYS, private communication, February 2023

for neutron therapy use a proton beam on a suitable target material such as Be or Li to produce neutrons, which is the principle of a spallation source. More details on the history of RT can be found in the publications referred to in the Further reading section, Sect. 5

1.2 Concepts and Types of Radiation Therapy Radiation therapy is general divided into external radiation beam therapy (ERBT) and internal radiation therapy (IRT). Whereas this separation refers to the source of radiation. Thus, if said source is located internally or externally from the patient. Please note that intraoperative radiation therapy (IORT), thus treating a cancer that has been exposed during surgery with ionizing radiation, is also considered part of ERBT.

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Internal Radiation Therapy

IRT relies on a surgical implantation of a radiation source near or inside a cancer, providing a defined dose to a locally restricted volume. IRT utilizes radioactive isotopes that emit continuously and omnidirectional, rather than on demand and directed beams, as in ERBT. Therefore, IRT is also referred to as Brachytherapy, whereas brachy is based on the Greek word brachys, meaning short and describes the therapy more precise. Sources used for this therapy, are mainly small and sealed isotopes that emit .β or low energy photon radiation, which allow to deposit the therapeutic dose within a short distance from the source. This way a lethal dose can be provided to the cancer, while tissues further away are mostly saved from exposure. The strong dose gradient is the main advantage of this therapy type. Various subdivision of this therapy have developed, which include temporary and permanent placement of the source, as well as hot loading and afterloading. The latter refers the process of loading the radiation source into an applicator that was surgically implanted to the patient earlier. While hot loading implies that said applicator is already loaded with an radioactive source, during the implantation. Advantages of brachytherapy are local application and restriction of the treatment volume. Additionally, the continuous application of the treatment dose at either low (.≤ 2Gy/h) or high rates (.≤ 12Gy/h) have lead to clinical success rates similar to EBRT [22, 34], while keeping exposure to healthy tissue low. Typical isotopes used are among others, .131 Cs,.125 I, .192 Ir and .103 Pd. Although under active research, .α sources are not used for brachytherapy [3], due to the short linear energy transfer (LET) of .α particles, therefore rendering the effective range in tissue to .< 1 mm.

1.2.2

External Radiation Beam Therapy

Modern ERBT is provided by some form of an accelerator and is the most used mode of therapy that is applied nowadays. The advantage compared to IRT is that the source of radiation is only active as long as the accelerator is active. Hence, deactivated accelerators do not pose a radiation risk. This makes it easier to place these devices within the premises of hospitals and treatment institutions. A major downside of ERBT is that healthy tissue is inevitably exposed to high doses of radiation. Therefore, careful treatment planning has become an essential part of contemporary external radiotherapy, as have radiation detectors to verify the planned outcome.

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1.3 Most Commonly Used Therapies The by far most commonly used type of external RT is based on X-rays. This is due to the comparably cheap and small footprint linacs used for this therapy. Furthermore, shielding of a facility is simple and only little activation of materials occurs. All this makes X-ray based RT the choice for most cancer types. It is further referred to as photon-, Röntgen-, or colloquially beam therapy. Various improvements and modifications exist for this therapy. Of which a few are described in this section. The most noteworthy improvements are the advances of medical imaging for RT. Today, virtually all radiotherapies are delivered based on Computer Tomography (CT), Magnetic Resonance (Tomography) Images (MRI), or similar techniques that are obtained before, during and after the therapy. These information allow to monitor and adjust the treatment continuously, which has enabled does reductions to healthy tissue significantly, while also increase the efficacy of modern X-ray therapy. Another improvement is computer assisted (tumor) tracking that allows to compensate for respiratory and patient movement to some extend. It further improves dose delivery, while reducing exposure to healthy tissue [37]. The next step is to actively track the tumor during the therapy and adjust the beam and dose profile while the therapy is being carried out. This requires specialized detectors and will be discussed later in more detail (Sect. 4.1). Other recent improvements are: Intensity Modulation Using beamlets to actively control shape and portion of the beam, allowing to further spare healthy tissue, while cancer tissue is treated. Stereotactic Irradiation Uses several (usually lower dose) beams from various directions, providing high dose at the convergence center, while reducing exposure of healthy tissue. Combination Therapy Is used in combination with other cancer therapies, such as surgical, chemo or gene therapy. Other Types of EBRT These are electron, proton, carbon and heavy ion therapies. Each with their individual advantages and disadvantages. The most notably advantage is that these types of therapy allow to control the energy of the particle in the patient precisely, which results in control of the location of the Bragg peak and with that the place of highest energy transfer in the patient. This leads to lower surface and healthy tissue dose and more precise dose delivery to the tumor volume. Conceptually this is depicted in Fig. 2, where the dose distribution of X-ray and proton therapy beams are shown in relation to one another. For X-ray therapy, the dose is highest slightly below the skin and is then continuously decreasing with increasing depth in the patient. The dose is further scaled so that the tumor region receives 100% of the target dose. As a consequence, are skin and shallow tissue doses higher than the target dose. In addition, is the tissue located after the tumor (from beam point of view) also exposed so significant dose. This is the reason why X-ray RT is

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Fig. 2 Dose distribution for X-ray and proton therapy in comparison. For X-ray therapy, a continuous attenuated dose profile (red line) is administered to the patient, including tissue before and after the tumor region. A much more confined dose profile can be achieved with proton therapy by spreading out the Bragg peak (SOBP, blue dashed line). [46]

performed from multiple angles and in numerous sessions (fractionated), to ensure that the overall dose of healthy tissue stays below an adverse threshold, while the accumulated dose to the tumor tissue reaches the prescribed dose to treat the tumor. In proton and other particle based therapies, the majority of the dose is deposited at the Bragg peak, with no further dose after it as the particle is stopped completely. Furthermore, the entrance dose is also reduced as comparably little energy is lost during shallow interaction in the tissue. The depth of the Bragg peak is controlled with slight adjustments in the energy of the particle acceleration, causing a spreading out the Bragg peak (SOBP), which enables precise dose administration to the tumor volume. Accelerators that can be used for particle therapy are however substantially more expansive, therefore leading to fewer devices. In Europe, were only 44 particle therapy accelerators listed in 2022, which includes all types of particle therapies [36]. Please note that the Bragg peak of an electron beam behaves differently and thus requires a different approach to administer a prescribed dose in a tumor region, while keeping it low for healthy tissue [21].

1.4 Modifications of Existing Radiotherapies Numerous modifications exist for RTs, with some being actively practiced and others still being at the stage of clinical studies. A few of the main research concepts are: Hypofractionated RT Increases the dose delivered per fraction by a factor of