Monte Carlo Modeling and Design of Photon Energy Attenuation Layers for >10× Quantum Yield Enhancement in Si-Based Hard X-Ray Detectors

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Article Monte Carlo Modeling and Design of Photon Energy Attenuation Layers for >10× Quantum Yield Enhancement in Si-Based Hard X-ray Detectors

Eldred Lee 1,2,*, Kaitlin M. Anagnost 1, Zhehui Wang 2 , Michael R. James 2, Eric R. Fossum 1 and Jifeng Liu 1,*

1 Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA; [email protected] (K.M.A.); [email protected] (E.R.F.) 2 Los Alamos National Laboratory, Los Alamos, NM 87545, USA; [email protected] (Z.W.); [email protected] (M.R.J.) * Correspondence: [email protected] or [email protected] (E.L.); [email protected] (J.L.)

Abstract: High-energy (>20 keV) X-ray photon detection at high quantum yield, high spatial resolution, and short response time has long been an important area of study in physics. Scintillation is a prevalent method but limited in various ways. Directly detecting high-energy X-ray photons has been a challenge to this day, mainly due to low photon-to-photoelectron conversion efficiencies. Commercially available state-of-the-art Si direct detection products such as the Si charge-coupled device (CCD) are inefficient for >10 keV photons. Here, we present Monte Carlo simulation results and analyses to introduce a highly effective yet simple high-energy X-ray detection concept with significantly enhanced photon-to-electron conversion efficiencies composed of two layers: a top high-Z photon energy attenuation layer (PAL) and a bottom Si detector. We use the principle of photon energy down conversion, where high-energy X-ray photon energies are attenuated down Citation: Lee, E.; Anagnost, K.M.; ≤ Wang, Z.; James, M.R.; Fossum, E.R.; to 10 keV via inelastic scattering suitable for efficient photoelectric absorption by Si. Our Monte Liu, J. Monte Carlo Modeling and Carlo simulation results demonstrate that a 10–30× increase in quantum yield can be achieved Design of Photon Energy Attenuation using PbTe PAL on Si, potentially advancing high-resolution, high-efficiency X-ray detection using Layers for >10× Quantum Yield PAL-enhanced Si CMOS image sensors. Enhancement in Si-Based Hard X-ray Detectors. Instruments 2021, 5, 17. Keywords: photonics; materials science; semiconductors; multidisciplinary; compound semiconduc- https://doi.org/10.3390/ tors; X-ray detection; image sensor; photon attenuation instruments5020017

Academic Editor: Antonio Ereditato 1. Introduction Received: 7 April 2021 Since the discovery of X-rays by Roentgen, the continuous expansion of X-ray tech- Accepted: 28 April 2021 Published: 30 April 2021 nology has transformed our society from materials science to biomedical applications. However, the capability gap for the efﬁcient and direct detection of high-energy X-ray

Publisher’s Note: MDPI stays neutral photons in the 20–50 keV range and beyond is challenging, which will prevent further with regard to jurisdictional claims in advancements in rising fields of technology such as the generic platform of X-ray imag- published maps and institutional affil- ing sensor technology and the next generation of synchrotron light source facilities [1–5]. iations. Scintillator-based methods are widely used in these types of facilities and high-energy X-ray detection technologies; however, they have major limitations such as decay time response and light yield [6,7]. Furthermore, the spatial resolution of such a method is limited due to the thickness required for the scintillator to absorb high-energy X-ray photons. There are also commercially available state-of-the-art X-ray detectors based on Si direct detection. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. For instance, the Si charge-coupled device (CCD) and CMOS image sensors, which are This article is an open access article commercially available in many formats, are known to be efficient in X-ray photon energies distributed under the terms and ≤10 keV and are typically most efficient in the 100 eV–10 keV range [8]. However, beyond conditions of the Creative Commons this energy, Si is notoriously inefficient in detecting X-rays as it is known to transmit the Attribution (CC BY) license (https:// majority of high-energy photons [8,9]. creativecommons.org/licenses/by/ There have been considerable efforts to overcome these issues and limitations by 4.0/). many researchers. One example of such work is a two-layer high-energy X-ray detec-

Instruments 2021, 5, 17. https://doi.org/10.3390/instruments5020017 https://www.mdpi.com/journal/instruments Instruments 2021, 5, 17 2 of 17

tor structure comprising a cm-scale-area and mm-scale-thick metal buildup layer on a semiconductor thin-film to obtain high energy deposition and high dose delivery for radiation therapy [10,11]. However, because this type of work could be unsuitable with small-form-factor commercial-off-the-shelf technologies (COTs), such as CMOS image sensors (CIS) and quanta image sensors (QIS) as mm- and cm-scale metal thickness, could cause significant X-ray crosstalk to adjacent pixels that might be 20–50 µm in pixel pitch [12]. Furthermore, the claim that has been made for the underlying principle of this prior work is that high-energy X-ray photons are converted to secondary electrons through Compton interaction in the top mm-scale metal buildup layer followed by the transport of these secondary electrons into the semiconductor thin-film layer for electron detection [10]. While this concept is intriguing, one questionable critical matter for our energy range of interest is that if the incident X-ray photon energies are relatively low compared to those intended for medical applications (MeV range), the low-energy secondary electrons (~1–10 keV range) could never escape the thick metal buildup layer after absorbing an X-ray photon as the corresponding electron mean free paths are rather small (<1 µm) in many materials [13]; therefore, the electrons could never make it to the bottom semiconductor thin-film layer for electron detection. Because of the relatively small travel ranges of electrons, even if the semiconductor thin-film layer for electron detection is decreased to µm-scale in terms of thickness, it is likely that the secondary electrons could still remain in the mm-scale-thick metal buildup layer. Similar to this example, a Si X-ray CT detector for MeV-range applications that utilizes 200 µm-thick tungsten (W) metal sheet as a down-converter placed between two Si detectors has been previously developed and takes advantage of secondary electrons [14]. However, due to the thickness of the W layer, such a concept would be incompatible with and unideal for COTS CIS and QIS. Another class of work focuses on structured photocathode designs that depend on external photoemission, the angle of X-ray photon absorption, and the collection of electrons produced by photon interactions using an external electric field. This approach has demonstrated up to 5% quantum yield (QY), which is defined [15–17] as:

# of primary photoelectrons collected QY = , (1) # of incident photons

In this article, primary photoelectrons are defined as those directly excited by X-ray photons prior to impact ionization, while secondary photoelectrons are those created by primary photoelectrons via impact ionization [16]. For almost 4 decades, QY from external photoemission has been roaming around 1–1.5%; therefore, the increase to 5% is commendable [17,18]. While the technique to reach the 5% QY is claimed to be suitable for higher X-ray photon energies at around 20–30 keV, one should note that the X-ray photon absorption coefficient will decay rapidly with the increase in incident photon energies, which eventually will lead to lower QY at higher incident photon energies [8,9,19]. Therefore, this technique may not be extended to higher X-ray photon energy ranges of interest (i.e., >20 keV). There also have been numerous recent advances in the development of high-Z X- ray detectors such as Ge- and Cr compensated GaAs (GaAs:Cr)-based detectors [20–22]. However, these materials have considerable fabrication drawbacks. For instance, there is a necessity to eliminate thermally generated carriers by cooling the material down to cryogenic temperatures for Ge-based high-energy X-ray detectors [20,21]. Furthermore, while GaAs:Cr-based detectors seem favorable, fabrication yield of good quality GaAs can be difficult [22]. There also have been significant advances in CdTe-based detectors, which is now one of the most common materials used in high-energy X-ray detection. Some of the CdTe- based detectors report 75–100% efficiency at 20–50 keV range; however, to reach such high efficiency, the thicknesses of CdTe must be in hundreds of microns and commercial state-of- the-art CdTe-based detectors currently use mm-scale-thick CdTe layers [10,23,24]. It should also be stressed that unlike Si CIS-based devices, CdTe-based detectors cannot be easily Instruments 2021, 5, 17 3 of 17

scaled into large arrays. Moreover, large semiconductor material thicknesses will ultimately restrict the response time of the devices. As a result, relatively thick film applications will not be ideal and suitable for small-form-factor COTs CIS and QIS-based devices. In addition to the aforementioned research work and advances in high-energy X-ray detection methods, Si calorimeters have also been in extensively studied. While there have been significant efforts on the development of the Si calorimeters, including integration with CMOS-based sensors, they are typically for large-area Si applications (i.e., cm2 and m2) and also for considerably higher energy photons or particles, mostly in the GeV range [25]. Scintillators are known to have high absorption efficiencies. Similar to recent devel- opments in CdTe-based detectors, the absorption efficiencies may be between 50% and 100%. Similar to CdTe-based detectors, the high efficiencies are reached by using hundreds of microns of scintillation materials and in many cases, they are achieved by using mm- and cm-thick layers [26,27]. However, besides absorption efficiency, the total efficiency of scintillators is important to be discussed. To calculate the total efficiency TE of scintillators, the following equation must be used:

TE = Dx × A × Ex × IQE (2)

where Dx is detector efficiency at an incident photon energy, A is absorption efficiency at an incident photon energy, Ex is first-order light extraction efficiency limited by total internal reflection, which is 1/4n2, n being the refractive index, and IQE is quantum efficiency of converting to UV/visible photons [26]. A very commonly used state-of-the-art scintillator is NaI(TI). When this scintillator is considered with 60 keV incident energy, 2 in diameter, and 2 in thickness, the corresponding values of Equation (2) are Dx = 0.97, A = 1, Ex = 0.073, and IQE = 0.15 to 0.30 [26,27]. Using these values, the TE of NaI (TI) scintillators with 60 keV incident X-ray photon energy can range between 1.06% and 2.12%. The low TE of a relatively thick scintillator describes the limitation of scintillators and if this thickness is decreased to µm-scale as our proposed concept, the TE will be significantly exacerbated. As it is demonstrated by the calculation above, the inadequate total efficiency is caused by the exceptionally low light extraction efficiency, which is limited by total internal reflection. Not only will the total efficiency be considerably reduced by such restriction, but also signal-to-noise ratio [28]. Recent efforts have sought to enhance the light extraction efficiency. A prime example of such efforts is the development of Bi4Ge3O12 scintillators with arrays of well-designed polymethyl-methacrylate (PMMA) hemispherical microlens that have led to a notable increase in the light extraction efficiency [28]. However, this noteworthy increase was only by a factor of 1.94–2.59, which would still leave the total efficiency substandard.

2. Concept of Photon Attenuation Layer (PAL) In this article, we present a new concept for the direct detection of high-energy X-ray photons by using a high-Z thin film, the “photon attenuation layer” (PAL), to attenuate the incident photon energy below 10 keV, thereby allowing more efficient absorption of down-converted X-ray photons by Si detectors underneath, or more generally, an “electron generation layer” (EGL). Throughout this article, the definition of QY corresponds to Equation (1), where the primary photoelectrons collected are those in Si EGL. Our Monte Carlo simulation results and analyses using Monte Carlo N-Particle Software (MCNP6.2) demonstrates 10–30× QY enhancement in the X-ray photon energy range of 20–50 keV. The conceptual design consists of two layers: a high-Z material PAL and a Si EGL, as shown in Figure1a. The two types of primary interaction mechanisms in PAL-EGL are photon energy down conversion due to inelastic scattering, followed by photoelectric absorption [29] (Figure1a). Because X-ray absorption and scattering cross-sections increase as atomic numbers increase, high-Z materials are chosen for the PAL [30]. In PAL, photons lose energies via single and multiple inelastic scattering events and eventually undergo notable redshift from the incident X-ray wavelength, leading to an effective X-ray photon energy attenuation down to ≤10 keV. It should be noted that X-ray photons only require Instruments 2021, 5, x FOR PEER REVIEW 4 of 18 Instruments 2021, 5, 17 4 of 17

absorption [29] (Figure 1a). Because X-ray absorption and scattering cross-sections in- creaseto go as throughatomic numbers a few increase, inelastic high scattering-Z materials processesare chosen for to the lose PAL energy [30]. In PAL, down to rather softer photons lose energies via single and multiple inelastic scattering events and eventually undergoX-ray spectralnotable redshift regime from prior the toincident absorption X-ray wavelength, [31]. This leading then allows to an effective Si to undergo X- photoelectric rayabsorption photon energy with attenuation a much down higher to ≤1 absorption0 keV. It should coefﬁcient, be noted that thereby X-ray photons signiﬁcantly improving onlythe require QY. Depending to go through on a few the inelastic Si thickness, scattering thereprocess couldes to lose also energy be additionaldown to photon energy ratherattenuation softer X-ray within spectral Si regime prior prior to the to absorption photon-to-electron [31]. This then conversion. allows Si to undergo Cascade processes such photoelectricas impact absorption ionization, with which a much could higher lead absorption to further coefficient, increase thereby in lower-energysignificantly electrons, occur improving the QY. Depending on the Si thickness, there could also be additional photon energyfollowing attenuation the photoelectric within Si prior absorption to the photon because-to-electron the conversion. average energy Cascade of pro- X-ray excited primary cessesphotoelectrons such as impact is ionization, on the orderwhich ofcould keV, lead while to further the increase average in energylower-energy required to create an electrons,electron-hole occur following pair (EHP) the photoelectric in Si via impactabsorption ionization because the isaverage only 3.65energy eV of [X32- –34]. It should be raynoted excited that primary in the photoelectrons proposedenergy is on the range order of of keV, interest, while the especially average energy with high-Zre- materials, the quired to create an electron-hole pair (EHP) in Si via impact ionization is only 3.65 eV [32– 34photoelectric]. It should be noted effect that is in the the mostproposed dominant energy range form of interest, of photon especially interaction. with high Compton- scattering Zmay materials, primarily the photoelectric occur between effect is the 50 most keV dominant and 3 MeV form ofand photon is the interaction. most dominant between Compton100 keV scattering and 150 may keV. primarily Because occur the between energy 50 k rangeeV and 3 of M interesteV and is the is between most dom- 20 keV and 50 keV, inantphotoelectric between 100 effectkeV and should 150 keV. be Because primarily the energy considered range of interest over Comptonis between 20 interaction [35]. In keVaddition, and 50 keV, it is photoelectric expected thateffect theshould PAL-EGL be primarily concept considered can over also Compton be integrated inter- with CIS- or QIS- action [35]. In addition, it is expected that the PAL-EGL concept can also be integrated withbased CIS- devices. or QIS-based A schematic devices. A schematic diagram diagram of the expectedof the expected CIS- CIS or- QIS-based or QIS-based device cross-section devicewith cross PAL-EGL-section integrationwith PAL-EGL is integration shown in is Figureshown in1 b.Figure 1b.

FigureFigure 1. (a 1.) Schematics(a) Schematics showing showing the mechanism the mechanism of high-Z PAL of-Si high-Z EGL detector PAL-Si design. EGL High detector- design. High-energy energy X-ray photons (shown with blue arrows) are incident to the top of the high-Z PAL. Inci- dentX-ray photons photons are down (shown-converted with (i.e. blue, redshifted, arrows) as are shown incident with red to arrows) the top via of inelastic the high-Z scatter- PAL. Incident photons ingare in down-convertedthe high-Z PAL and undergo (i.e., redshifted, efficient photoelectric as shown absorption with red by arrows) Si; (b) representation via inelastic ofscattering in the high-Z thePAL expected and cross undergo-section efﬁcient of backside photoelectric illuminated CIS absorption- or QIS-based by device Si; ( bwith) representation PAL-EGL inte- of the expected cross- gration; 1 is high-Z PAL, 2 is a thin (<100 nm) backside passivation oxide (e.g., SiO2) that can be addedsection between of backside PAL and illuminatedSi for practicality CIS- but orthe QIS-based overall QY s devicehould not with be affected PAL-EGL because integration; 1 is high-Z PAL, down-converted X-ray photons can readily penetrate through the oxide layer, 3 is optional im- 2 is a thin (<100 nm) backside passivation oxide (e.g., SiO2) that can be added between PAL and Si plants or epitaxial growth for surface pinning, 4 are pixelated carrier storage wells, and 5 is front sidefor pixel practicality readout circuitry. but the overall QY should not be affected because down-converted X-ray photons can readily penetrate through the oxide layer, 3 is optional implants or epitaxial growth for surface pinning,While 4the are overall pixelated underlying carrier principle storage of wells, photon and energy 5 is frontdown side conversion pixel readout could be circuitry. somewhat similar to scintillator-based methods, it should be emphasized that this approach Whileis distinctive the overallin that the underlying attenuated photons principle still ofremain photon in the energy X-ray spectral down re- conversion could be gime as opposed to the UV and visible regime. Unlike scintillators, the down conversion primarilysomewhat relies similar on inelastic to scintillator-based scattering with high- methods,Z atoms, and it therefore should beno emphasizedexotic and ex- that this approach pensiveis distinctive bulk crystals in (as that in the case attenuated of scintillators) photons are needed still for remain the PAL in la theyers. X-rayIn fact, spectral regime as theopposed PAL layers to the can UV be polycrystalline and visible regime. or even amorphous Unlike scintillators, thin films, which the down are much conversion primarily relies on inelastic scattering with high-Z atoms, and therefore no exotic and expensive bulk crystals (as in the case of scintillators) are needed for the PAL layers. In fact, the PAL layers

can be polycrystalline or even amorphous thin films, which are much easier to fabricate than bulk crystal scintillators. The response time is also no longer limited by the optical spontaneous emission lifetime in scintillators, potentially allowing for ultrafast response since X-ray photon energy down conversion time via X-ray fluorescence and/or inelastic scattering is typically much shorter than the optical fluorescence time in scintillators. This conceptual design may also offer integration capabilities to Si CIS- or QIS-based devices for high resolution X-ray imaging. A key fundamental difference between the proposed PAL concept and scintillators is the interaction volumes between high-energy X-ray photons and materials. The interaction Instruments 2021, 5, 17 5 of 17

volume of scintillators is typically in the order of hundreds of microns and in many cases, mm- or cm-scale due to material thicknesses as previously stated [26]. It is likely that scintillator-based detectors have higher absorption efﬁciencies as mentioned in the introduction, but this is due to the larger interaction volumes. The primary end-use goal of the proposed concept is for Si CIS- or QIS-based devices, meaning that scintillator-based methods will be unsuitable for these types of image sensors as scintillator layers will require bulk layers.

3. Monte Carlo Simulations & Results For the purpose of this article, the thickness of the high-Z PAL was set as 1 µm for most data to simply demonstrate and emphasize that a thin high-Z material layer can tremendously enhance high-energy X-ray photon energy attenuation, leading to efficient photoelectric absorption in Si. On the other hand, PAL thicknesses can be optimized corresponding to the thicknesses of Si and incident X-ray photon energies, which will be discussed towards the end of this article. Si layer thicknesses were chosen according to the typical range between CIS/QIS and commercial Si wafers. High-Z semiconductor materials such as CdTe, CdZnTe (CZT), Bi2Te3, and PbTe can be used as PAL materials due to their chemical stability and material availability for thin film solar cells, thermoelectric materials, or infrared detectors [36–39]. The listed high-Z semiconductor materials are also known to be more compatible with CMOS-based devices [40–42]. Semiconductors have been specifically chosen as they can serve a double purpose by simultaneously down-converting photon energies and generating electrons [30]. For this article, we primarily explored PbTe because Pb has a higher atomic number than Cd. Additionally, PbTe is easier to fabricate than CdTe and CZT due to the difficulties in growing homogeneous defect-free thin films of CdTe and CZT [43,44].

3.1. Verification of Photon Energy Attenuation in High-Z PAL To verify the concept of photon energy attenuation in thin-film PAL using high-Z semiconductor materials, energy distributions of the photons transmitted through the high-Z PAL have been modeled with MCNP6.2. The MCNP simulation was conducted on 105 incident photons, and the transmitted photon energy histograms are plotted in 0.1 keV bins. We confirm that the transmitted photons have a much lower energy than the incident ones, and a notable fraction will have energies <10 keV to facilitate absorption by Si as shown in Figure2a,b for 20 and 30 keV incident X-ray photons after transmitting through a 1 µm PbTe PAL, respectively, both using 50 µm pixel size. These figures do not show the energy range of 0–1 keV since there is a default artificial photon energy cutoff around 1 keV in our MCNP simulation and important effects for scattering leading to lower energies are not yet included in MCNP6.2 photon transport methods, resulting in photon energies below the cutoff to not be calculated [45,46]. This cutoff tends to underestimate the photon absorption in Si because the mass attenuation coefficients of Si decrease with photon energy, as shown in Figure2a,b to demonstrate overlaps with the down-converted X-ray photon spectra [13,47]. From Figure2, we find that the photon energies are down-converted mainly into two distinctive regimes after transmitting through 1 µm-thick PbTe PAL: (1) A nearly continuous low energy spectrum at 1–5 keV, where Si has large mass attenuation coefficients for efficient absorption. This regime is induced by multiple inelastic scattering of incident photons; (2) Sharp and discrete energy peaks corresponding either to the characteristic X-ray emissions of Pb or Te atoms [48–50], or transition energies corresponding to energy losses from incident energies, otherwise known as edges. The characteristic X-ray emissions of Pb or Te atoms also correspond with X-ray fluorescence (XRF) spectrum of Pb and Te [50,51]. Full tables that list the origins of a majority of the significant peaks are provided in AppendicesA andB. This regime is induced by photons that have only experienced from one to a few inelastic scattering events. Instruments 2021, 5, x FOR PEER REVIEW 6 of 18

(1) A nearly continuous low energy spectrum at 1–5 keV, where Si has large mass attenuation coefficients for efficient absorption. This regime is induced by multiple inelastic scattering of incident photons; (2) Sharp and discrete energy peaks corresponding either to the characteristic X-ray emissions of Pb or Te atoms [48–50], or transition energies corresponding to energy losses from incident energies, otherwise known as edges. The characteristic X-ray emissions of Pb or Te atoms also correspond with X-ray fluorescence (XRF) spectrum of Pb and Te [50,51]. Full tables that list the origins of a majority of the significant peaks are provided in Appendices A and B. This regime is induced by photons that have only experienced from one to a few inelastic scattering events. For the case of 20 keV incident photons, several major peaks in regime (2) are still located at <10 keV, which can be effectively absorbed by Si. Therefore, both regimes (1) and (2) contribute significantly to enhanced X-ray absorption in Si in this case. As the Instruments 2021, 5, 17 incident photon energy increases above 30 keV, most of these characteristic X-ray peaks 6 of 17 are located at >10 keV (Figure 2b), and efficient absorption of down-converted photons at 1–5 keV in regime (1) become the dominant mechanism of QY enhancement for Si detectors.

FigureFigure 2. 2. X-X-rayray photon photon energy energy distribution distribution histograms histograms after transmitting after through transmitting a 50 µm throughpixel a 50 µm pixel size size and 1 μm-thick PbTe PAL layer for (a) 20 keV and (b) 30 keV incident photons. The total num- µ andber of 1 incidentm-thick photons PbTe is 10 PAL5, and layer the histograms for (a) 20 are keV plotted and using (b) 30 0.1 keV keV energy incident bins. photons. Each sig- The total number of incidentnificant discrete photons peak isin 10the5 histogram, and the is histograms identified/labeled are plottedwith either using characteristic 0.1 keV X- energyray emis- bins. Each significant discretesion of Pb/Te peak atoms in the (XRF), histogram or incident is photon identified/labeled energy subtracted with by the either energy characteristic losses from the X-ray emission of Pb/Te absorption edges of Pb/Te. Mass attenuation coefficients of Si as a function of photon energy are atomsalso shown (XRF), in both or plots. incident This m photonass attenuation energy coefficient subtracted spectrum by the indicates energy that losses X-ray photon from the absorption edges ofenergies Pb/Te. need Mass to be attenuationattenuated below coefficients 10 keV for efficient of Si as absorption a function by Si. of photon energy are also shown in both plots. This mass attenuation coefficient spectrum indicates that X-ray photon energies need to be attenuated below 10 keV for efficient absorption by Si.

For the case of 20 keV incident photons, several major peaks in regime (2) are still located at <10 keV, which can be effectively absorbed by Si. Therefore, both regimes (1) and (2) contribute signiﬁcantly to enhanced X-ray absorption in Si in this case. As the incident photon energy increases above 30 keV, most of these characteristic X-ray peaks are located at >10 keV (Figure2b), and efﬁcient absorption of down-converted photons at 1–5 keV in regime (1) become the dominant mechanism of QY enhancement for Si detectors. AppendixC includes two photon transmissivity (%T) vs. incident X-ray photon energy plots and compare %T calculated using Beer’s Law and %T determined using MCNP without boundary limits for 200 µm-thick Si and 1 µm PbTe. It can be clearly seen that for the case of 200 µm Si, %T calculated using Beer’s Law and MCNP are very similar due to Si being low-Z and does not greatly contribute to photon energy down conversion via inelastic scattering, while for the case of 1 µm PbTe, the theoretical and simulated values demonstrate fairly large discrepancies at lower incident energies. At lower energies, an increased amount of inelastic scattering events results in more photon energy down conversion in PbTe, a high-Z material, causing it to absorb the lower-energy down- converted photons and leading to less transmission of photons. As the incident energy increases, the amount of inelastic scattering events will decrease, allowing simulated %T to be closer to the theoretical Beer’s Law values and closing the gap between the discrepancies.

3.2. Quantum Yield Enhancement in Si Further including 5 µm, 50 µm, and 200 µm-thick Si layers in the MCNP simulation with 105 incident photons, Figure3a,b compare the QY of Si hard X-ray detectors with and without PAL as a function of incident photon energy based on the deﬁnition in Equation (1). The CIS pixel size is 50 × 50 µm2 in the simulation, and the X-ray photons scattered outside Instruments 2021, 5, x FOR PEER REVIEW 7 of 18

Appendix C includes two photon transmissivity (%T) vs. incident X-ray photon energy plots and compare %T calculated using Beer’s Law and %T determined using MCNP without boundary limits for 200 µm-thick Si and 1 µm PbTe. It can be clearly seen that for the case of 200 µm Si, %T calculated using Beer’s Law and MCNP are very similar due to Si being low-Z and does not greatly contribute to photon energy down conversion via inelastic scattering, while for the case of 1 µm PbTe, the theoretical and simulated values demonstrate fairly large discrepancies at lower incident energies. At lower energies, an increased amount of inelastic scattering events results in more photon energy down conversion in PbTe, a high-Z material, causing it to absorb the lower-energy down-converted photons and leading to less transmission of photons. As the incident energy increases, the amount of inelastic scattering events will decrease, allowing simulated %T to be closer to Instruments 2021, 5, 17 the theoretical Beer’s Law values and closing the gap between the discrepancies. 7 of 17

3.2. Quantum Yield Enhancement in Si Further including 5 μm, 50 μm, and 200 μm-thick Si layers in the MCNP simulation thewith pixel 105 incident region photons, is no longer Figures tracked/counted.3a,b compare the QY Figureof Si hard3a,b X-ray demonstrate detectors with that incorporating aand 1 µ withoutm-thick PAL PAL as a layerfunction can of effectivelyincident photon increase energy thebased QY on ofthe Si definition detectors in Equa- by 10–30× depending tion (1). The CIS pixel size is 50 × 50 μm2 in the simulation, and the X-ray photons scattered onoutside the the incident pixel region photon is no energylonger tracked/counted. and the Si thickness. Figures 3a,b Even demonstrate though that the in- mass attenuation coefﬁcientcorporating a of1 μm Si-thick decreases PAL layer with can photoneffectively energy increase (Figurethe QY of2 ),Si detectors Figure3 byb shows10– that the QY enhancement30× depending on contributed the incident photon by PbTe energy PAL and actually the Si thickness. increases Even withthough the the incident mass X-ray photon energy.attenuation In coefficient other words, of Si decreases devices with with photon PAL energy show (Figure much 2), less Figure QY 3b degradation shows that at higher X-ray photonthe QY enhancement energies. contributed This feature by PbTe is especially PAL actually helpful increases for with high-energy the incident X X-ray-ray detection. For photon energy. In other words, devices with PAL show much less QY degradation at 5higherµm, X 50-rayµ photonm, and energies. 200 µ mThis Si, feature theQY is especially with 1 helpfulµm PbTe for high PAL-energy (solid X-ray lines) de- ranges between 6.54%tection. andFor 5 33.48%μm, 50 μm for, and 20 200 keV μm photons. Si, the QY with Remarkably, 1 µm PbTe PAL even (solid the lines) thinnest ranges 5 µm Si with PAL demonstratesbetween 6.54% and ~2 ×33.48%higher for 2 QY0 keV than photons. the thickest Remarkably, 200 evenµm Sithe without thinnest 5 PAL. µm Si Furthermore, QYs withwith PAL PALs demonstrates are all higher ~2× higher than QY thethan ~5% the thickest QY at 200 7.5 µm keV Si without incident PAL.X-ray Further- photon energy, as more, QYs with PALs are all higher than the ~5% QY at 7.5 keV incident X-ray photon demonstratedenergy, as demonstrated by state-of-the-art by state-of-the-art photoemission photoemission X X-ray-ray detectors detectors [17]. [17].

FigureFigure 3.3. (a)( aQY) QY in Si in as Sia function as a function of incident of photon incident energy photon with 1 energyµm PbTe withPAL (solid 1 µm lines) PbTe PAL (solid lines) and withoutand without 1 µ 1m μm PbTe PbTe PAL PAL (dashed lines) lines) and and with with 5 μm 5, 50µ m,μm 50, andµ m,200 andμm Si 200 andµ 50m µm Si and 50 µm pixel; (b) QY pixel; (b) QY enhancement (factor) vs. incident photon energy for the three different Si thick- enhancementnesses to represent (factor) that 1 µm vs. PbTe incident PAL can photon remarkably energy increase for the the QY three as opposed different to having Si thicknesses to represent thatno PAL. 1 µ m PbTe PAL can remarkably increase the QY as opposed to having no PAL.

With 200 µm-thick Si, it can be seen from AppendicesD andE that <50 µm pixel pitches can lead to a quick roll-off of QY with 1 µm PbTe PAL because the incident X-ray photon is scattered outside the original pixel region, which can indicate a significant crosstalk at <50 µm pixel pitches. In AppendixF, a plot representing the number of exiting photons from 1 µm PbTe PAL vs. pixel pitch can be seen. This confirms that at <50 µm pixel sizes, a significant amount of photons would already be prematurely scattered outside of the original pixel region even prior to reaching the Si layer, leading to the aforementioned indication of significant crosstalk for <50 µm pixels and the quick roll-off of QY. In AppendixE, both plots exhibit two distinctive kinks in QY vs. pixel pitch at 50 µm and 150 µm pixels. The kink shown on 150 µm pixel is caused by the limited lateral scattering distance for X-ray absorption and primary photoelectron excitation at smaller pixels, and the kink shown on 50 µm pixel is due to the crosstalk at <50 µm pixels (i.e., the incident X-ray photon is scattered outside the original pixel after a limited number of scattering events). Furthermore, by comparison, using 200 µm-thick Si without 1 µm PbTe PAL, it can be seen from AppendicesD andE the magnitude of QY decreases much faster with the decrease in pixel size than in the case of having the PAL layer. In fact, without the PAL layer, the QY already almost decreases by half as the pixel size shrinks from 100 µm to 50 µm pixel, in contrast to a less than 15% decrease for the case with PAL. This result indicates that the PAL layer not only helps to drastically enhance the QY, but also helps to reduce the crosstalk by confining the incident X-ray photons and photoelectrons within the original pixel because the X-ray photon energy is down-converted more efficiently. Therefore, there will be a much higher QY especially for ≥50 µm pixel sizes and less Instruments 2021, 5, 17 8 of 17

limitation in the spatial resolution of direct detection. In addition, there could be lateral scattering of X-ray photons and the generation of primary photoelectrons, especially in larger pixels; therefore, higher efﬁciency would be seen with larger pixels. As a result, the proposed concept and design would be the most suitable for pixel sizes ≥50 µm. QY will eventually saturate at signiﬁcantly larger pixels with or without 1 µm PbTe PAL as shown in AppendicesC andD, with the plot with the case of using 1 µm PbTe PAL in AppendixD still showing 3–10× high QY at >200 µm pixel sizes. Furthermore, while the proposed concept focuses on 1 µm PbTe PAL due to the easiness of material fabrication compared to CdTe, CdTe should also be discussed as it is a common material used in high-energy X-ray photon detection, as previously mentioned. Moreover, 1 µm CdTe PAL is also effective and can provide another option for PAL material. The QY plot for 1 µm CdTe PAL, 50 × 50 µm2 pixel size, and 5 µm, 50 µm, and 200 µm Si can be seen in AppendixG. It is clear that 1 µm CdTe PAL results in less QY than 1 µm PbTe PAL, which is expected due to Cd being lower-Z than Pb, resulting in less inelastic scattering events, but it still provides 6–19x QY enhancement from the case of having no PAL.

3.3. Impact Ionization Process The average energies corresponding to the primary photoelectrons in Si from Figure3a solid lines are found to be in the keV range; therefore, impact ionization processes due to regenerative actions should take place. As previously stated, impact ionization processes to promote electrons in the valence band to the conduction band can further provide signiﬁcant increase to the number of lower-energy electrons that will be generated within Si. The number of primary photoelectrons upon X-ray excitation associated with the QY and the approximate total # of electrons after impact ionization are shown in Table1. To approximate the number of electrons post-impact ionization processes, the following equation can be taken into consideration: avg. primary photoelectron energy in Si [eV] × # ofprimary photoelectrons in Si EGL = # of electrons in Si after impact ionization 3.65eV , (3) EHP

In Equation (3), the average energies and the number of the primary photoelectrons generated in Si prior to additional impact ionization processes can be determined using MCNP6.2 for devices with 1 µm PbTe PAL (i.e., corresponding to the solid lines in Figure3a). The product of these two should be divided by 3.65 eV, the aforementioned average energy required to generate an EHP in Si [3,24–26], to approximate the ultimate total number of electrons in Si after impact ionization. Table1 shows the comparison between the number of X-ray excited primary photoelectrons before impact ionization (which were used to determine the QY in Figure3a) and the approximate number of electrons post-impact ionization using Equation (3). All cases lead to an approximate regenerative increase in lower-energy electrons by a factor of 103–104.

3.4. PAL Thickness Optimization It was previously mentioned that optimal thicknesses of PAL corresponding to incident X-ray photon energies and Si thicknesses can be determined. To conﬁrm this statement, different thicknesses of PbTe PAL were placed on top of 5 µm and 200 µm Si at 20 keV, 30 keV, and 50 keV incident X-ray photon energies and 50 µm pixel to demonstrate that PAL thicknesses can be optimized according to different incident energies and Si thicknesses. In Figure4a, with 5 µm Si and the three different incident energies, a peak between 1 µm and 1.5 µm PbTe PAL is seen, indicating that 1 µm–1.5 µm PbTe PAL will result in highest QY with 5 µm Si at the corresponding incident energies. In Figure4b, with 200 µm Si and the three different incident energies, a peak between 0.5 µm and 0.75 µm PbTe PAL is seen; therefore, 0.5 µm–0.75 µm PbTe PAL will result in the highest QY with 200 µm Si. Notably, a QY approaching 40% can be achieved for 20 keV incident photons, and 16% for 35 keV Instruments 2021, 5, 17 9 of 17

incident photons. These results further conﬁrm the potentials of PAL layers for integration with Si-based high-energy X-ray detectors.

Table 1. Comparison between the number of photoelectrons (before impact ionization) per 105 incident X-ray photons and ultimate # of electrons after impact ionization in 5 µm, 50 µm, and 200 µm Si with 1 µm PbTe PAL and 50 µm pixel. Average electron energies in Si are still in the keV; therefore, further impact ionization processes can be undergone to provide at least three orders of magnitude increase in the # of lower-energy electrons as shown on the far-right column of the table. As expected, thicker Si leads to higher number of electrons.

Incident Si Avg. Electron # of Primary Photoelectrons Approx. Ultimate # of Energy Thickness Energy in Si Pre-Impact Ionization Electrons Post- (keV) (µm) (keV) (Figure3a Solid Lines) Impact Ionization 20 5 4.83 6535 8.65 × 106 30 5 6.79 2373 4.41 × 106 50 5 11.00 805 2.43 × 106 20 50 4.39 21,123 2.54 × 107 30 50 5.75 8799 1.39 × 107 50 50 8.45 4162 9.64 × 106 Instruments 2021, 5, x FOR PEER REVIEW 20 200 4.24 33,478 3.89 × 107 10 of 18 30 200 5.43 14,260 2.12 × 107 50 200 7.73 6156 1.30 × 107

Figure 4. QY of (a) 5 µm Si and (b) Si with different thicknesses of PbTe PAL at 20 keV, 30 keV, and Figure 4. QY of (a) 5 μm Si and (b) Si with different thicknesses of PbTe PAL at 20 keV, 30 keV, 50 keV incident X-ray photon energies and 50 µm pixel. Optimal PbTe PAL thickness is seen between and 50 keV incident X-ray photon energies and 50 µm pixel. Optimal PbTe PAL thickness is seen 1 µm and 1.5 µm for 5 µm Si, and between 0.5 µm and 0.75 µm for 200 µm Si. between 1 μm and 1.5 μm for 5 µm Si, and between 0.5 μm and 0.75 μm for 200 μm Si.

4. Concluding Remarks In this article, we introduced a new high-energy X-ray direct detection concept capable of enhancing the QY by 10–30× for Si-based X-ray detectors using high-Z PAL, with a great potential to well surpass the performance of state-of-the-art X-ray detectors based on Si CCD or photocathodes and well-established scintillation- and CdTe-based methods. There have been recent significant efforts to increase the total efficiency of scintillation- based methods, but the enhancements observed so far have been unremarkable and the total efficiency still remains low due to the light extraction efficiency being limited by total internal reflection. The proposed concept may also have the capabilities to be optimized and applied to CdTe-based photodetectors to reduce the required thicknesses as the current state-of-the-art CdTe-based methods require considerably thick layers of the material, which will limit the response time of the devices. This simple yet highly effective device structure and its underlying principle of X-ray photon energy down-conversion have the potential to transform X-ray detection, e.g., spatial resolution and response time. Addi- tional schemes of PAL and EGL layer material choices and optimizations are possible as the overall innovation of the proposed concept is the integration of PAL with EGL, while the PAL can be other adequate high-Z materials not necessarily limited to semiconductors and the EGL can be Si, CdTe, or other adequate semiconductor materials. It should also be noted that with the PAL-EGL concept, the potential exploitation of the photons with incident energies as well as the incoming energy-attenuated photons from the PAL to the EGL may be viable. The former would rely on the choices of materials and their thicknesses. The latter can be readily inferred from the number of photo-electrons in the EGL after impact ionization. To further determine the original incident photon energy, one

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4. Concluding Remarks In this article, we introduced a new high-energy X-ray direct detection concept capable of enhancing the QY by 10–30× for Si-based X-ray detectors using high-Z PAL, with a great potential to well surpass the performance of state-of-the-art X-ray detectors based on Si CCD or photocathodes and well-established scintillation- and CdTe-based methods. There have been recent significant efforts to increase the total efficiency of scintillation-based methods, but the enhancements observed so far have been unremarkable and the total efficiency still remains low due to the light extraction efficiency being limited by total internal reflection. The proposed concept may also have the capabilities to be optimized and applied to CdTe-based photodetectors to reduce the required thicknesses as the current state-of-the-art CdTe-based methods require considerably thick layers of the material, which will limit the response time of the devices. This simple yet highly effective device structure and its underlying principle of X-ray photon energy down-conversion have the potential to transform X-ray detection, e.g., spatial resolution and response time. Additional schemes of PAL and EGL layer material choices and optimizations are possible as the overall innovation of the proposed concept is the integration of PAL with EGL, while the PAL can be other adequate high-Z materials not necessarily limited to semiconductors and the EGL can be Si, CdTe, or other adequate semiconductor materials. It should also be noted that with the PAL-EGL concept, the potential exploitation of the photons with incident energies as well as the incoming energy-attenuated photons from the PAL to the EGL may be viable. The former would rely on the choices of materials and their thicknesses. The latter can be readily inferred from the number of photo-electrons in the EGL after impact ionization. To further determine the original incident photon energy, one could potentially utilize the differences in attenuated photon energy distribution shown in Figure2 . For example, 20 keV incident photons have a substantial probability of being attenuated to 4–10 keV, yet 30 keV incident photons have little probability to fall into this energy range after being attenuated by the PbTe PAL layer. Based on this kind of input, data-driven approaches such as machine learning, deep learning, and artificial intelligence that are often used for medical imaging applications, especially those that use scintillation crystals, could be trained/applied to determine the most probable incident photon energy before passing through PAL [52,53]. Furthermore, with the capability of monolithic integration with Si CIS, the PAL-enhanced image sensors can also pave the way towards a wide field- of-view X-ray camera designs for synchrotron and X-ray free electron laser light source applications [3,4]. The modeling in this work will guide future experimental verification towards high-resolution, high-efficiency X-ray detection using PAL-enhanced Si CIS and as a strong candidate to be utilized in the future advancements of X-ray camera designs crucial for synchrotron and X-ray free electron laser light source applications.

Author Contributions: PAL modeling work was performed by E.L. under the supervisions of J.L. and Z.W. and work pertinent to photon energy distribution and impact ionization were contributed by K.M.A. and E.R.F. M.R.J. provided guidance for initial simulation work. The manuscript was prepared by E.L. under the guidance of J.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the Experimental Science Program (C3) at Los Alamos National Laboratory under the subcontract number 537679 and basic agreement number 537992 with The Trustees of Dartmouth College. It was also supported by the United States Department of Energy National Nuclear Security Administration Laboratory Residency Graduate Fellowship (DOE NNSA LRGF) under the award numbers DE-NA0003864 and DE-NA0003960. Los Alamos National Laboratory is managed by Triad National Security, LLC for the United States Department of Energy. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest. Instruments 2021, 5, 17 11 of 17

Appendix A Table of peaks in 0.1 keV bin photon energy distribution plot representing energies corresponding to energy losses from incident energies (edges) or characteristic X-ray energies (XRF): 1 µm PbTe PAL at 20 keV incident energy. Energy losses from incident are the differences between incident energies and peak energies. Peaks corresponding to edges are shown in red and peaks corresponding to XRF are shown in black. The incident energy peak is shown in green. The remaining blue peaks are attenuated photons via inelastic scattering processes. The broadened structures from 15 keV to 18 keV are presumably Instruments 2021, 5, x FOR PEER REVIEW 12 of 18 photons that have not undergone enough inelastic scattering processes in PAL to lose signiﬁcant energy.

FigureFigure A1. A1. TransmittedTransmitted photon energy distribution histogramhistogram fromfrom FigureFigure2 a2a with with the the origins origins of of the themajority majority ofthe of the signiﬁcant significant peaks. peaks.

TableTable A1. List of origins of the significant signiﬁcant peaks numbered in Figure A1..

PeakPeak Energy Energy EnergyEnergy Loss Loss from from TransitionTransition Corresponding to PeakPeak # # XRFXRF Peak Peak (keV)(keV) IncidentIncident (keV) (keV) CorrespondingLoss to Loss 6 15.1 4.9 L1 edge (Te) or M (Pb) - 6 15.1 4.9 L1 edge (Te) or M (Pb) - 5 512.7 12.7 7.3 7.3- - LLβ1β1or or L Lββ22 (Pb)(Pb) 4 410.6 10.6 9.4 9.4- - LLαα11 (Pb) (Pb) 3 7.0 13.0 L edge (Pb) - 3 7.0 13.0 L3 3edge (Pb) - 2 4.8 15.2 L2 edge (Pb) - 2 4.8 15.2 L2 edge (Pb) - 1 4.2 15.8 L1 edge (Pb) - 1 4.2 15.8 L1 edge (Pb) -

Appendix B Appendix B Table of peaks in 0.1 keV bin photon energy distribution plot representing energies Table of peaks in 0.1 keV bin photon energy distribution plot representing energies corresponding to energy losses from incident energies (edges) or characteristic X-ray corresponding to energy losses from incident energies (edges) or characteristic X-ray en- energies: 1 µm PbTe PAL at 30 keV incident energy. Energy losses from incident are the ergies: 1 µm PbTe PAL at 30 keV incident energy. Energy losses from incident are the differences between incident energies and peak energies. Peaks corresponding to edges are differences between incident energies and peak energies. Peaks corresponding to edges shown in red and peaks corresponding to XRF are shown in black. The incident energy are shown in red and peaks corresponding to XRF are shown in black. The incident energy peak is shown in green. The remaining blue peaks are attenuated photons via inelastic peak is shown in green. The remaining blue peaks are attenuated photons via inelastic scattering processes. The broadened structures from 25 keV to 28 keV are presumably scattering processes. The broadened structures from 25 keV to 28 keV are presumably photons that have not undergone enough inelastic scattering processes in PAL to lose photons that have not undergone enough inelastic scattering processes in PAL to lose sig- signiﬁcant energy. nificant energy.

Instruments 2021, 5, x FOR PEER REVIEW 12 of 18

Figure A1. Transmitted photon energy distribution histogram from Figure 2a with the origins of the majority of the significant peaks.

Table A1. List of origins of the significant peaks numbered in Figure A1.

Peak Energy Energy Loss from Transition Corresponding to Peak # XRF Peak (keV) Incident (keV) Loss 6 15.1 4.9 L1 edge (Te) or M (Pb) - 5 12.7 7.3 - Lβ1 or Lβ2 (Pb) 4 10.6 9.4 - Lα1 (Pb) 3 7.0 13.0 L3 edge (Pb) - 2 4.8 15.2 L2 edge (Pb) - 1 4.2 15.8 L1 edge (Pb) -

Appendix B Table of peaks in 0.1 keV bin photon energy distribution plot representing energies corresponding to energy losses from incident energies (edges) or characteristic X-ray energies: 1 µm PbTe PAL at 30 keV incident energy. Energy losses from incident are the differences between incident energies and peak energies. Peaks corresponding to edges are shown in red and peaks corresponding to XRF are shown in black. The incident energy peak is shown in green. The remaining blue peaks are attenuated photons via inelastic Instruments 2021, 5, 17 12 of 17 scattering processes. The broadened structures from 25 keV to 28 keV are presumably photons that have not undergone enough inelastic scattering processes in PAL to lose significant energy.

Instruments 2021, 5, x FOR PEER REVIEW 13 of 18 Figure A2. Transmitted photon energy distribution histogram from Figure2b with the origins of the majority of the signiﬁcant peaks.

Figure A2. Transmitted photon energy distribution histogram from Figure 2b with the origins of Tablethe majority A2. Listof the of significant origins peaks of the. signiﬁcant peaks numbered in Figure A2.

Table A2. List of originsPeak Energyof the significantEnergy peaks numbered Loss from in FigureTransition A2. Corresponding Peak # XRF Peak Peak Energy(keV) Energy Loss Incidentfrom Transition (keV) Correspondingto Loss Peak # XRF Peak 10(keV) 25.1Incident (keV) 4.9to Loss L1 edge (Te) or M (Pb) – 10 925.1 17.04.9 13.0L1 edge (Te) or M (Pb) L3 edge (Pb)-- – 9 817.0 14.813.0 15.2L3 edge (Pb) L2 edge (Pb)-- – 7 14.2 15.8 L edge (Pb) – 8 14.8 15.2 L2 edge (Pb) 1 -- 6 12.7 17.3 – Lβ1 or Lβ2 (Pb) 7 14.2 15.8 L1 edge (Pb) -- 5 12.3 17.7 – Lβ4 (Pb) 6 12.7 17.3 -- Lβ1 or Lβ2 (Pb) 4 10.6 19.4 – Lα1 (Pb) 5 312.3 9.317.7 20.7-- –Lβ4 (Pb) L` or Lτ (Pb) 4 210.6 4.119.4 25.9-- –Lα1 (Pb) Lβ3 (Te) 3 19.3 3.820.7 26.2-- –Lℓ or L휏 (Pb) Lα1 (Te) 2 4.1 25.9 -- Lβ3 (Te) 1 3.8 26.2 -- Lα1 (Te) Appendix C Appendix%T vs.C incident X-ray photon energy for 200 µm Si (left) and 1 µm PbTe (right). %T obtained%T vs. usingincident theoretical X-ray photon Beer’s energy Law for 200 calculations µm Si (left) and and 1 Monteµm PbTe Carlo (right). (MC) %T simulations are similarobtained using for 200 theoreticalµm Si Beer’s and Law discrepancies calculations and are Monte demonstrated Carlo (MC) simulations for 1 µm are PbTe, especially at similar for 200 µm Si and discrepancies are demonstrated for 1 µm PbTe, especially at lowerlower incident incident energies. energies. As Si is As low Si-Z, is MC low-Z, will not MC demonstrate will not demonstratephoton energy down photon energy down conversion via via inelastic inelastic scattering. scattering. However, However, in 1 µm in PbTe, 1 µm as PbTe, less inelastic as less scattering inelastic scattering events occurevents occur at higher at higher incident incident energies, energies, the the gap gap between between the discrepancies the discrepancies will decrease will decrease and the discrepanciesand the discrepancies will will remain remain relatively relatively largelarge at at lower lower energies energies due dueto more to inelastic more inelastic scattering. scattering.

Figure A3. A3. %T%T vs. inciden vs. incidentt X-ray photon X-ray energies photon for energies 200 µm Si for (left 200) andµ m1 µm Si PbTe (left ()right and). 1%Tµ mis PbTe (right). %T is calculated using using Beer’s Beer’s Law and Law MCNP. and MCNP. Appendix D QY vs. pixel pitch without (Figure A4) and with (Figure A5) 1 µm PbTe PAL and 200 µm Si thicknesses at 20 keV, 30 keV, and 50 keV incident energies. Pixel sizes were varied from 2 µm to 100 µm. The quick roll-off in QY at 50 µm pixel can indicate a significant crosstalk at <50 µm pixel pitches. As a result, the proposed concept would be the most

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Appendix D QY vs. pixel pitch without (Figure A4) and with (Figure A5) 1 µm PbTe PAL and InstrumentsInstruments 2021 2021, 5, ,5 x, xFOR FOR PEER PEER REVIEW REVIEW 1414 of of 18 18 200 µm Si thicknesses at 20 keV, 30 keV, and 50 keV incident energies. Pixel sizes were varied from 2 µm to 100 µm. The quick roll-off in QY at 50 µm pixel can indicate a signiﬁcant crosstalk at <50 µm pixel pitches. As a result, the proposed concept would suitablebesuitable the most for for ≥ ≥50 suitable50 µm µm pixels. pixels. for ≥ It 50It can canµm be be pixels. see seenn that that It can the the bemagnitude magnitude seen that of of the QY QY magnitude with with decreasing decreasing of QY pixel withpixel isdecreasingis greater greater in in pixelthe the case case is greater of of having having in the no no case 1 1 µm µm of PbTe havingPbTe PAL. PAL. no 1 µm PbTe PAL.

22000µµmm-t-hthicickk S Si iw w/o/o 1 1µµmm P PbbTTee P PAALL 7.70.0%0% 202k0ekVeV 6.60.0%0% 303k0ekVeV 505k0ekVeV

5.50.0%0% )

) 4.40.0%0%

(

Y Q Q 3.30.0%0%

2.20.0%0%

1.10.0%0%

0.00.0%0% 00 1010 2020 3030 4040 5050 6060 7070 8080 9090 10100 PPixiexle Pl Piticthch ( µ(mµm) )

FigureFigureFigure A4. A4.A4. QY QYQY vs. vs.vs. pixel pixel pitch pitch (2 (2–100(2––100100 µm) µµm)m) without without 1 1 µm µmµm PbTe PbTe PAL PAL and and 200 200 µm µµmm Si Si at at 20 20 keV, keV, 30 3030 keV, keV,andkeV, 50and and keV 50 50 incidentkeV keV incident incident X-ray X X photon-ray-ray photon photon energies. energies energies. .

22000µµmm-t-hthicickk S Si iw w/ /1 1µµmm P PbbTTee P PAALL 454.50.0%0% 2200kekeVV 404.00.0%0% 3300kekeVV 5500kekeVV 353.50.0%0%

303.00.0%0% )

) 252.50.0%0%

(

Y Q Q 202.00.0%0%

151.50.0%0%

101.00.0%0%

5.50.0%0%

0.00.0%0% 00 1010 2020 3030 4040 5050 6060 7070 8080 9090 10100 PPixiexle Pl Piticthch ( µ(mµm) ) FigureFigureFigure A5. A5.A5. QY QYQY vs. vs.vs. pixel pixelpixel pitch pitchpitch (2 (2–100(2––100100 µm) µµm)m) with withwith 1 11 µm µµmm PbTe PbTePbTe PAL PAL and and 200 200 µµm µmm Si Si at at 20 20 keV, keV, 3030 30 keV,keV, keV, and and50and keV 50 50 keV incidentkeV incident incident X-ray X X- photonray-ray photon photon energies. energies energies. .

AppendixAppendixAppendix E EE QYQYQY vs. vs. p pixel pixelixel p pitch pitchitch with with withoutoutout ( Figure(Figure (Figure A6 A6 A6) )and and) and with with with ( Figure(Figure (Figure A7 A7 )A7 )1 1 µm )µm 1 µPbTe PbTem PbTe PAL PAL PAL and and and200 200 µm200µm Si µSi mthicknesses thicknesses Si thicknesses at at 2 200 atk keV,eV, 20 3 keV,300 k keV,eV, 30 and keV,and 5 5 and00 k keVeV 50 incident incident keV incident energies. energies. energies. Pixel Pixel sizes sizes Pixel were were sizes varied varied were fromvariedfrom 2 2 µm fromµm to to 2500 500µm µm µm to. 500.It It can canµm. be be seen It seen can that that be theseen the magnitude magnitude that the magnitude of of QY QY with with of decreasing decreasing QY with decreasingpixel pixel pitch pitch isis greater greater in in the the case case of of having having no no 1 1 µm µm PbTe PbTe PAL. PAL. At At significantly significantly larger larger pixels, pixels, especially especially beyondbeyond 200 200 µm µm pixels, pixels, the the QYs QYs eventually eventually saturate saturate for for both both cases cases of of with with and and without without 1 1 µmµm PbTe PbTe PAL. PAL.

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pixel pitch is greater in the case of having no 1 µm PbTe PAL. At signiﬁcantly larger pixels, InstrumentsInstruments 2021 2021, 5, ,5 x, xFOR FOR PEER PEER REVIEW REVIEW µ 1515 of of 18 18 especially beyond 200 m pixels, the QYs eventually saturate for both cases of with and without 1 µm PbTe PAL.

22000µµmm-t-hthicickk S Si iw w/o/o 1 1µµmm P PbbTTee P PAALL 202.00.0%0% 202k0ekVeV 181.80.0%0% 303k0ekVeV 50keV 161.60.0%0% 50keV

141.40.0%0%

121.20.0%0%

)

(

1( 0.00%

Y 10.00%

Q Q 8.80.00%0%

6.60.00%0%

4.40.00%0%

2.20.00%0%

0.00.00%0% 00 5050 10100 151050 20200 252050 30300 353050 40400 454050 50500 PPixiexle Pl Pitcithc h(µ (mµm) )

Figure A6. QY vs. pixel pitch (2–500 µm) without 1 µm PbTe PAL and 200 µm Si at 20 keV, 30 keV, FigureFigure A6. A6. QY QY vs. vs. pixel pixel pitch pitch (2 (2–500–500 µm) µm) without without 1 1µm µm PbTe PbTe PAL PAL and and 200 200 µm µm Si Si at at 20 20 keV, keV, 30 30 keV,andkeV, and 50 and keV 50 50 keV incidentkeV incident incident X-ray X X- photonray-ray photon photon energies. energies energies. .

Figure A7. QY vs. pixel pitch (2–500 µm) with 1 µm PbTe PAL and 200 µm Si at 20 keV, 30 keV, and FigureFigure A7. A7. QY QY vs. vs. pixel pixel pitch pitch (2 (2–50–500 0µm) µm) with with 1 1µm µm PbTe PbTe PAL PAL and and 200 200 µm µm Si Si at at 20 20 keV, keV, 30 30 keV, keV, 50 keV incident X-ray photon energies. andand 50 50 keV keV incident incident X X-ray-ray photon photon energies energies. . Appendix F AppendixAppendix F F Number of Exiting Photons from 1 µm PbTe PAL vs. Pixel Pitch at 20 keV, 30 keV, Number of Exiting Photons from 1 µm PbTe PAL vs. Pixel Pitch at 20 keV, 30 keV, and 50Number keV incident of Exiting energies. Photons Pixel from sizes 1 wereµm PbTe varied PAL from vs. 2Pixelµm toPitch 100 µatm. 20 It k caneV, be30 seenkeV, and 50 keV incident energies. Pixel sizes were varied from 2 µm to 100 µm. It can be seen thatand at50 aroundkeV incident 50 µm, energies. the number Pixel ofsizes exiting were photons varied from signiﬁcantly 2 µm to decreases100 µm. It ascan the be pixel seen that at around 50 µm, the number of exiting photons significantly decreases as the pixel sizethat decreasesat around at50 a µm much, the quicker number slope, of exiting indicating photons that significantly with <50 µm decreases pixels, considerable as the pixel size decreases at a much quicker slope, indicating that with <50 µm pixels, considerable amountssize decreases of photons at a much are prematurely quicker slope, scattered indicating outside that ofwith the < original50 µm pixels, pixel region considerable before amounts of photons are prematurely scattered outside of the original pixel region before reachingamounts theof photons Si layer, are resulting prematurely in much scattered lower QY outside and signiﬁcant of the original crosstalk pixel issues. region before reachingreaching the the Si Si layer, layer, resulting resulting in in much much lower lower QY QY and and significant significant crosstalk crosstalk issues. issues.

InstrumentsInstruments 20212021, ,55, ,x 17 FOR PEER REVIEW 1615 of of 18 17 Instruments 2021, 5, x FOR PEER REVIEW 16 of 18

Figure A8. # of exiting photons from 1 µm PbTe PAL at 20 keV, 30 keV, and 50 keV incident X-ray Figure A8. # of exiting photons photons from from 1 1 µmµm PbTe PbTe PAL PAL at at 20 20 keV, keV, 30 30 keV, keV, and 50 keV keV incident incident X X-ray-ray photon energies vs. pixel pitch (2–100 µm). photonphoton energiesenergies vs.vs. pixel pitchpitch (2–100(2–100 µµm)m)..

AppendixAppendix G G QYQY vs. vs. incident incident X X-rayX-ray-ray photon photon energy energy (left) (left)(left) and andand QY QYQY enhancement enhancementenhancement (factor) (factor)(factor) vs. vs.vs. incident incidentincident 2 XX-rayX-ray-ray photon photonphoton energy energy (right)(right) (right) withwith with 11 µ1 µm mµm CdTe CdTe CdTe PAL, PAL, PAL, 50 50 ×50 50× × 50 µ50m μm μm2 pixel 2pixel pixel size, size, size, and and and 5 µ 5m, 5 μm μm 50,µ ,50 m,50 μmandμm, ,and 200and 200µ 200m μm Si.μm UsingSi. Si. Using Using 1 µ m1 1 µm CdTeµm CdTe CdTe as PAL as as PAL PAL enhances enhances enhances QY QY by QY 6–19xby by 6 6––19 from19xx f romfrom not nothaving not having having PAL. PAL. PAL. The TheenhancementThe enhancement enhancement is lower is is lower lower than than than PbTe PbTe PbTe PAL, PAL, PAL, which which which is expected is is expected expected due due due to to lower-Z to lower lower- ofZ-Z of Cdof Cd Cd leading leading leading to tolessto less less scattering scattering scattering events. events. events.

FigureFigure A9. A9. QYQY vs. vs. incident incident photon photon energy energy with with and and without without 11 µmµm CdTe CdTe PAL PAL shown shown with with solid solid and Figure A9. QY vs. incident photon energy with and without 1 µm CdTe PAL shown with solid and dashed lines, respectively (left) and QY enhancement (factor) vs. incident photon energy for dashedand dashed lines, lines, respectively respectively (left )(left and) and QY enhancementQY enhancement (factor) (factor) vs. incidentvs. incident photon photon energy energy for threefor three different Si thicknesses to represent that 1µm CdTe PAL can increase the QY as opposed to differentthree different Si thicknesses Si thicknesses to represent to represent that 1 thatµm CdTe1µm CdTe PALcan PAL increase can increase the QY the as QY opposed as opposed to having to having no PAL (right). nohaving PAL no (right PAL). (right).

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