Charge Sharing Assessment and Active Collimation in Monolithic Arrays of Silicon Drift Detectors

Charge sharing (CS) between pixels is a significant concern in X-ray spectroscopy detectors based on monolithic arrays of silicon drift detectors (SDDs) when a photon is absorbed near a pixel edge. Traditional mechanical collimation mitigates CS but decreases the active area of the detector. This is particularly true for small-pixel detectors, where the mechanical collimator shields a significant portion of the active area and, moreover, becomes quite complex to be manufactured for small apertures. In this work, we carry out a study of CS in SDDs and introduce active collimation as an alternative to mechanical collimation, leveraging key parameters of signals at the output of the charge-sensitive amplifier (CSA), to identify CS events occurring within a defined coincidence window (CW) in neighboring pixels. To validate the technique, we first conducted a quantitative assessment of the impact of CS on a 16-element monolithic SDD module with 2-mm-side square pixels using a focused pulsed laser. We then tested an active collimation algorithm on this detector configuration during a spectroscopic measurement with an uncollimated 55Fe source, demonstrating its capability in recovering CS events and reconstructing them as Mn-K $\alpha $ peak events. This active collimation approach, in contrast to mechanical collimation, not only enhances the effective active area while achieving a substantial reduction in the background continuum of the spectrum, but also recovers information inevitably lost in uncollimated detectors due to intrinsic CS effects.

SECTION I. Introduction

Monolithic arrays of silicon drift detectors (SDDs) have gained significant attention in a variety of applications, including X-ray spectroscopy and X-ray imaging, due to their excellent energy resolution and high count rate capability [1], [2], [3], [4], [5], [6]. The monolithic configuration offers advantages such as ease of assembly and minimization of dead area which, in turn, grants the possibility to embed a high number of sensitive elements to enhance the output count rate within a compact size.

Despite their many advantages, however, monolithic arrays of SDDs are also subject to the phenomenon known as charge sharing (CS). CS is a significant concern in X-ray spectroscopy and imaging applications, as multichannel instruments based on monolithic SDD arrays may register multiple partial signals on different detector channels if a single photon is absorbed near a pixel edge. This can cause the charge cloud generated in the X-ray sensor to spread across multiple channels where it is collected in neighboring anodes.

CS events, where a single photon’s energy is deposited across multiple pixels, contribute to the background continuum in the spectrum from the noise peak to the photon energy, due to the fact that the split charge packets drift toward different anodes, resulting in reduced energy in the final spectrum [7], [8].

This issue is traditionally addressed with mechanical collimation, that involves placing a physical barrier on the edge of each pixel, resulting in a reduction of the background as incomplete charge collection due to CS is avoided. However, mechanical collimation inevitably causes a loss in the total active area of the sensor, reducing overall efficiency. This issue is particularly relevant when dealing with multielement SDDs that have a high number of channels in a compact area: as the number of channels increases, so does the dead area, i.e., the fraction of the detector covered by the mechanical collimator, due to the fact that the width of the region interested by CS does not scale proportionally to pixel dimension.

CS is a significant issue in many silicon sensors, particularly in pixel and strip detectors, which are mainly used to reconstruct the trajectory of charged particles or to measure the spatial distribution of X-rays (especially in photon-counting mode) [8], [9], [10], [11], [12]. In these sensors, which measure the position of interaction of a single particle, CS lowers the intensity of signals that have to be detected and increase their multiplicity, making the design of the readout electronics more challenging. However, in this case, CS can be leveraged to enhance the positioning accuracy of these detectors beyond the intrinsic resolution of the detector elements.

To address the challenges arising from CS in pixel silicon detectors, alternative solutions to mechanical collimation have been proposed, includingon-chip hardware algorithms andoff-chip correction methods applied to measured data, as detailed in [13]. These approaches often involve estimating the total charge by analyzing fractional signals and attributing a hit to the pixel exhibiting the highest charge deposition. Alternatively, pattern recognition techniques, such as searching the center of gravity of the charge clouds, have been suggested [14], [15], [16].

Some existing works, such as [17], [18], [19], and [20], implement the sum of signals from adjacent pixels, presenting circuit implementations aimed at resolving the challenge of losing information about a photon hit position and its energy. It is noteworthy, however, that none of these solutions has been specifically optimized for spectroscopy in SDDs.

Active collimation, meaning the use of hardware and software-based techniques that do not involve a mechanical collimator, offers a number of advantages over traditional mechanical collimation. For instance, this method of collimation eliminates the need for physical barriers, preserving in principle the full active area of the detector. This is particularly beneficial for small-pixel-size detectors where mechanical collimation can result in significant area loss. Additionally, active collimation offers greater flexibility in tailoring to specific application requirements. However, its implementation can be more complex compared to mechanical collimation, and it may not completely eliminate CS events.

CS recovery, namely reconstructing events involving CS, employs techniques like rise time (RT) analysis and coincidence analysis to enhance efficiency in SDDs and mitigate background in the spectrum.

In this work, we first analyze the CS phenomenon on an SDD array, then we present an off-line implementation of active collimation in monolithic arrays of SDDs, based on an algorithm that leverages the RT of signals at the output of the charge-sensitive amplifier (CSA). This algorithm is designed to identify CS events occurring within a defined coincidence window (CW) in neighboring pixels, and employ signal amplitude summation for their subsequent reconstruction.

The article is organized as follows: Section II introduces the SDD module used for the experimental measurements, conducted with both a pulsed laser system and a ⁵⁵Fe source. Section III presents the experimental setup realized for these measurements, the data acquisition and elaboration pipeline, and the assessment of the area in the SDD affected by CS. Section IV introduces two main active collimation methods that were explored in this work, while Section V presents the related discussion of results. Conclusions are drawn in Section VI.

SECTION II. ARDESIA Detection Module

The ARDESIA project aims to develop a state-of-the-art X-ray spectrometer for high-count rate synchrotron applications. Designed for a wide range of scientific applications, such as X-ray fluorescence (XRF) spectroscopy, XRF microscopy (XFM), and X-ray absorption fine structure (XAFS), the ARDESIA spectrometer covers an energy range from 0.2 to 20 keV [21].

ARDESIA-16 in particular is a multichannel X-ray spectrometer based on a monolithic 16-element SDD array coupled with four custom four-channel CUBE CSAs operating within a pulsed reset regimen, periodically resetting the charge accumulated on its feedback capacitance due to leakage current [22], [23], [24]. ARDESIA-16 is specifically optimized to achieve a high-count rate ($\gt {\mathrm {1~Mcps}}$ /channel) and good energy resolution (e.g., below 150 eV full width at half maximum at peaking times faster than 200 ns) for XRF detection. The detection modules used in the ARDESIA-16 spectrometer are based on 16-channel monolithic SDD matrices which have been designed and produced at Fondazione Bruno Kessler (Trento, Italy).

The single pixel features a square geometry, with 5-mm-side configurations (total die area of $24\times 24$ mm) designed for the spectrometer and 2-mm-side modules (total die area of $12\times 12$ mm) developed for research purposes, as illustrated in Fig. 1(a). The detectors exhibit different thickness options, ranging from 450 to $800~\mu $ m and $\mathrm {1000~\mu \text { m} }$ , with larger thicknesses that extend the energy range in which the detector is efficient [25].

Fig. 1.

Detection modules of ARDESIA-16 consist of $4 \times 4$ arrays of square SDDs, where each element has an area of either $5\times 5$ mm (left) or $2\times 2$ mm (right). (a) Uncollimated modules. (b) Collimated modules. (c) Spectra on were obtained with a 5-mm-side detection module, before and after collimation. The implementation of a mechanical collimator, although a robust solution that allows spectrum background reduction, results in a reduction in the total active area of the detector.

In this context, CS poses a significant challenge, particularly in detectors characterized by small pixel pitch and thicker substrates, due to the shape of the internal electric field.

To mitigate the effects of CS, the 5-mm-side ARDESIA-16 detectors mount molybdenum collimators featuring a $\mathrm {500~\mu \text { m} }$ grid size, successfully diminishing the spectrum background, as shown in Fig. 1. However, it is crucial to acknowledge that this measure results in a reduction of more than 20% of the total active area, as detailed in Table I. The impact of an equivalent collimator on the 2-mm side module would be even more substantial (45% reduction in the total active area), rendering mechanical collimation impractical.

TABLE I Effects of Mechanical Collimation in the ARDESIA-16 SDD Modules

Therefore, we conducted an evaluation of the area on the SDD affected by CS in the 2-mm-pitch SDD array. Subsequently, we developed an algorithm for the identification and recovery of CS events, leveraging key parameters such as amplitude, RT, and time coincidence. This algorithm was extensively tested and validated on the same module, demonstrating significant capabilities in recovering CS events and reconstructing them as full-energy peak events.

SECTION III. CS Characterization

To evaluate the impact of CS and assess the performance of offline filtering algorithms, experimental measurements were conducted using an ARDESIA-16 detection module with 2-mm pixel pitch. Two different sources were employed: a pulsed laser source for a preliminary assessment of the detector area affected by CS, and a ⁵⁵Fe X-ray source for a detailed analysis.

The experimental setup for characterizing the SDD is illustrated in Fig. 2. The detection module was housed in a light-tight aluminum box to minimize the effect of ambient light, and maintained at a relative humidity below 5% using silica beads.

Fig. 2.

Characterization setup of the detection module for pulsed laser source. (a) Side view of the setup highlighting the SDD aluminum case, pulsed laser system, and three-axis translating stage. (b) Top view of the setup highlighting electronics readout and power supply unit.

A thermoelectric cooler (TEC) coupled to a liquid cooled heat sink was employed to maintain the SDD temperature at a controlled value of $- 25~^{\circ }$ C. Moreover, a custom-designed power supply unit (TESLA [26]) was used to bias the setup PCB which, in turn, was used to manage the signal conditioning of the preamplifier outputs, deliver a programmable threshold-sensitive reset signal to all preamplifiers, and provide ultralow-noise reference and supply voltages to the preamplifiers and the SDD matrix.

All signals were acquired and saved using a four-channel HDO6104B oscilloscope from Teledyne Lecroy [27] with different settings depending on the source. For capturing the ⁵⁵Fe events, the oscilloscope was triggered on single events allowing the acquisition of events in a CW at a 500 Msps sampling rate. The oscilloscope’s sequence acquisition and data saving capabilities enabled the acquisition of 100 waveforms simultaneously, resulting in approximately four million waveforms stored in 1 TB of memory. In both cases, the CSA output signal was collected for neighboring channels.

A. Pulsed Laser Measurements

The detector was irradiated with a focused laser beam to perform a preliminary evaluation of the CS entity and to accurately assess the region at the edge of the pixels where CS occurs, delivering the laser beam to the SDD in controlled positions. Fig. 2 depicts the setup used for this purpose.

A Thorlabs NPL41B [28] nanosecond pulsed laser system with 405 nm wavelength, coupled to an achromatic microspot UV focusing objective to achieve $4~\mu $ m spot size, was mounted on a three-axis manual translation stage in order to scan the SDD surface with $10~\mu $ m steps for the assessment of the CS region. The setup is specifically designed to deliver a microspot laser beam to the SDD in controlled positions.

The CUBE outputs were visualized and recorded using the oscilloscope (Fig. 3), and subsequently processed in MATLAB environment [29]. For each position of the laser beam, several voltage ramps at the output of the CUBE preamplifier were acquired, each ramp being the output between two reset pulses and containing multiple laser-generated events. This approach was essential in obtaining statistical insights into the photogenerated charge behavior at different points on the SDD surface. The height and RT values reported in Fig. 4 represent averages from multiple measurements.

Fig. 3.

CUBE response after the laser trigger at different laser spot positions in a single channel. (a) Anode. (b) Corner. (c) Edge. A noticeable trend is observed: the farther away from the anode, the longer the RT. Additionally, when CS occurs at the edge between multiple pixels, the event amplitude on a single channel is visibly lower.

Fig. 4.

Parameters of the signals generated by the focused laser beam are presented as a function of the absolute laser beam position within the SDD. The external border of the SDD is considered as the 0 mm reference. Multiple events were captured for each step position, enabling us to obtain statistics and represent the average value and standard deviation of amplitude and RT. (a) Event amplitude. A schematic view of the portion of the detector involved in the analysis is shown. The arrow denotes the path of the laser beam. (b) Event RT.

Throughout this work, the RT was calculated as the time taken for the step-like event at the output of the CSA to transition between the 10% and 90% points of its amplitude.

The algorithm used to process the acquired waveforms from the pulsed laser system involved a series of steps to identify, isolate, and characterize the events. The initial phase involved the automatic identification of all events through the computation of the first derivative. This step also allowed the identification and removal of ramp resets. Following the rough identification and isolation of each laser-generated event, an interpolation was applied to a section of the ramp before the event itself, allowing the removal of the ramp trend in the data. Subsequently, a thorough data cleaning and filtering process was implemented, wherein detected events with amplitudes lower than 1 mV, indistinguishable from noise, were systematically discarded.

The algorithm then progressed to compute the second derivative of the detrended events, aiming to pinpoint their precise inflection point, which served as the event timestamp.

On each detrended event, a trapezoidal filter [30], [31], [32] was applied with a peaking time of 300 ns and flat top of $\mathrm {1~\mu \text { s} }$ , for the computation of the event amplitude and RT.

Fig. 3 shows isolated and detrended events following a laser trigger at different positions in a single pixel of the monolithic SDD array, highlighting a visible pattern: when CS occurs, the charge carriers are spread out over multiple pixels and collected by neighboring anodes, and they therefore take longer to drift, resulting in a lower event amplitude and longer RT registered on each channel.

B. CS Region Assessment

By systematically scanning the surface of the SDD along the horizontal direction from its external border, denoted in Fig. 4 as 0 mm, toward the center of the detector using the focused laser beam, we observed a noteworthy relationship between the event amplitude and the irradiation position. The same measurements were repeated translating the laser beam along the vertical direction, exhibiting a specular behavior to the ones conducted horizontally, and along the diagonal direction moving toward a channel anode, as reported in Fig. 5. To retrieve the events, we collected the CSA output signal of neighboring channels. Specifically, we found that, as the laser moved closer to the edge between two neighboring channels, the amplitude of events recorded by the first irradiated pixel decreased, as the other increased proportionally. At the exact middle point between the two channels, the amplitude in both was the exact half of the one registered when the anodes were irradiated. This behavior suggests that, with a filter discriminating events occurring in CW based on their RT, the CS events on neighboring channels can be identified and summed, therefore retrieving their amplitude as useful events.

Fig. 5.

Amplitude of laser-generated events beam as a function the laser spot position translated in diagonal direction. Here, the corner among the four central channels of the SDD is considered as the 0 mm reference, and the laser beam is translated toward the anode of channel 8.

This behavior exhibits correlation to the RT, as the charge carriers generated from laser interactions add the borders between channels, affected by CS, had to travel a longer distance to reach the collection electrode, leading to slower RT.

Through a detailed examination of these results, we pinpointed a region of around $\mathrm {75~\mu \text { m} }$ impacted by CS along each side of a pixel edge, constituting approximately 14% of the total channel area. This finding suggests that CS can significantly affect the performance of monolithic arrays of SDDs. However, given that CS events are associated with specific features such as longer RT, reduced amplitude, and occurrence in a finite time window, these characteristics can be exploited to identify and correct for CS events.

C. ⁵⁵Fe Measurement Setup and Data Analysis

A standard ⁵⁵Fe calibration source was employed to provide uncollimated irradiation to the entire surface of the SDD array. Single events were captured using the oscilloscope, triggered by the slew rate of the step-like signal. The acquisition was focused on individual events rather than entire ramps, enabling the extraction of statistics from 4 million events. Fig. 6 shows a typical event in coincidence acquired on two different channels. The oscilloscope operated at a sampling rate of 500 Msps, capturing a duration of $\mathrm {5~\mu \text { s} }$ with 2500 samples at a resolution of 2 ns/sample.

Fig. 6.

CUBE output signal for a ⁵⁵Fe event on two adjacent channels occurring in a CW.

Since events were recorded using a four-channel oscilloscope, it provided information only on the triggering channel, identified as channel 8 [see Fig. 7(c)] throughout this work, and three neighboring channels instead of four (or eight if considering the channels neighboring by the corners). This constraint in our analysis could be addressed with a specialized digital pulse processor (DPP) in future studies.

Fig. 7.

(a) Histograms of amplitude and (b) RT of events captured on four neighboring channels in the SDD. The oscilloscope triggering on events collected by channel 8 implies that the other three channels observe events only when they are already in coincidence. This consists of a preliminary CW inherent to the measurement process and explains the relatively lower count of events compared to channel 8 for the other three channels. (c) Schematic view of the SDD channels involved in the analysis.

Fig. 7 presents histograms of amplitudes and RTs of events obtained through this measurement setup. The trigger on single events in channel 8 establishes an initial time window: neighboring channel events were exclusively captured during this time window, resulting in fewer events and a higher background in the spectra of these adjacent channels. Simultaneously, we assessed the RT, observing that background events tended to exhibit longer RTs, while photopeak events generally displayed RTs between 50 and 100 ns. The RT of X-ray events resulted to be shorter than the RT of events induced with the laser (Fig. 4), that exhibit a minimum RT around 120 ns. This difference is probably due to the different interaction mechanism of the laser photons at 405 nm wavelength within the SDD, with respect to X-ray photons emitted by a ⁵⁵Fe source [33]. The different interaction leads to a difference in charge signals produced.

A similar process to the one described in Section III-A was employed for data processing in order to extract meaningful information from acquired waveforms.

The data processing pipeline involves several steps, executed for each waveform and channel in MATLAB environment: after data import, we discarded waveforms saturated on any oscilloscope channel. Event identification shares a similar process with the pulsed laser measurements, except for reset removal: initially, it includes computing the second derivative of each output signal to determine the time stamp, identified as the inflection point of the step-like signal. Then, we implemented a pile-up rejection (PUR) filter by discarding events with timestamps closer than a set value. We discarded noise artifacts and interpolated the ramp for event detrending, leaving a signal similar to the one in Fig. 6.

The amplitude was computed with a trapezoidal filter with $\mathrm {1~\mu \text { s} }$ flat top and $\mathrm {1~\mu \text { s} }$ peaking time. Only events that met minimum amplitude and RT thresholds, equal to 1 mV and 20 ns, respectively, were considered valid, while those failing these criteria (less than 1% of total recorded events) were treated as noise and discarded. In the final step, calibration was performed by plotting histograms of the amplitude of events occurring on each channel, and applying Gaussian interpolation to the resulting spectra in order to determine the Mn-K$\alpha $ peak centroids. Subsequently, calibration coefficients were computed to align these centroids, effectively calibrating the spectra.

The resulting values of amplitude and RT indicate a correlation, with longer RTs corresponding to smaller amplitudes in CS events. In Fig. 8, the correlation graph between amplitude and RT for events collected by channel 8 illustrates this relationship.

Fig. 8.

Correlation graph explaining the relationship between amplitude and RT of the step-like signals at the output of the CSA collected by channel 8. If we look at the part characterized by lower amplitude and longer RT, we observe the region where CS occurs. Additionally, distinct areas corresponding to Mn-K$\alpha $ and Mn-K$\beta $ are clearly visible at approximately 28 and 32 mV of amplitude, with RTs below 100 ns. Note the change in the colorbar scale in the zoomed region.

SECTION IV. Active Collimation Methods

Motivated by the need for effective CS rejection methods, we explored two potential solutions. First, we implemented a filter rejecting events with RT longer than a user-defined value, which already exists in some commercial DPPs. Second, we developed a new method, integrating the analysis of the coincidences between channels with the RT information. This new approach aims to identify events detected within a finite time window on neighboring channels, classify them as CS events, and potentially recover and sum them as useful events in the final spectrum.

A. Maximum RT Filter

Some commercial DPPs such as XGLab DANTE [34] incorporate an algorithm that rejects events with RT longer than a specified value, known as maximum RT filter (Fig. 9). Traditionally employed for PUR, this algorithm could in principle be applied to CS rejection as well, as suggested by our analysis detailed in Section III-C.

Fig. 9.

Flowchart illustrating the two explored methods, the traditional maximum RT filter (left), and our CS recovery algorithm (right). The inset demonstrates, in red, the filtering impact on a single pixel with square geometry, emphasizing how the maximum RT filter on the left excludes even valid events detected on the channel diagonal, while the CS Recovery Algorithm on the right not only preserves events on the diagonal by rejecting only genuine CS events, but also recovers some CS events, significantly increasing the active area.

To assess the real-time filtering capabilities, measurements were conducted using an uncollimated ⁵⁵Fe X-ray source on the setup illustrated in Fig. 2.

The DANTE DPP was used for the acquisition of an initial dataset, and real-time filtering based on maximum RT was applied using the integrated DPP firmware. For comparison, a second dataset was acquired with the four-channel oscilloscope, and filtering was implemented in MATLAB following the flowchart illustrated in Fig. 9.

Fig. 10(a) and (b) displays different spectra for both datasets obtained using the filter based on the maximum accepted RT. For both acquisition systems, spectra obtained with longer maximum RTs (e.g., 280 ns) not only present Mn-K$\alpha $ peaks with the maximum amplitude but also a significant background. Conversely, applying a more strict filter (e.g., 96 ns) effectively reduced not only the background but also the number of counts in the Mn-K$\alpha $ peak. Likely, stricter filters limit the active area to a circular region around the anode, excluding useful photons absorbed along the diagonal of the pixel.

Fig. 10.

Spectra acquired on channel 8 with different values of maximum RT filter, using (a) DANTE DPP or (b) four-channel oscilloscope, show the effect of applying the filter at different RT thresholds. (c) Peak-to-tail ratio is plotted with respect to the maximum accepted RT. The goal is to identify a maximum RT value that maintains a sufficiently high peak-to-tail ratio. The analysis is presented in blue and orange for datasets obtained with the oscilloscope and the DPP, respectively. (d) Normalized integral of the Mn-K$\alpha $ peak is illustrated across varying maximum RT values. A low RT threshold leads to a decrease in the peak, indicating the exclusion of valid events.

After performing waveform analysis as in Section III to reconstruct the event energy and build the spectra, we found that our maximum RT filter is effective in discarding event with RT longer than a set value, specifically 200 ns. This threshold value was chosen based on the analysis presented in Fig. 10: the aim was a tradeoff between achieving a high peak-to-tail ratio (defined as the ratio between the counts of the photopeak at 5.898 keV and the average number of counts between 5.26 and 5.32 keV) while also maintaining the full integral counts under the Mn-K$\alpha $ peak.

Spectra from both datasets, after applying this filter with a 200 ns threshold, exhibited nearly complete peaks with high peak-to-tail ratios, indicating that very few useful events were discarded.

Despite its advantages, this filter has the major drawback of reducing the pixel efficiency by excluding events that interact further away from the anode, especially on the diagonal of square pixels, that are not yet affected by CS.

On the other hand, our novel algorithm (Fig. 9), which will be further explained in Section IV-B, implements CS identification and recovery. This algorithm not only excludes those events that genuinely involve CS, preserving events on the diagonal, but also allows for the recovery of CS events as valid events, that are added to the spectrum.

B. CS Identification and Recovery Algorithm

When a charge packet splits and is collected by different SDD anodes, the arrival times observed at the anodes fall within a finite CW defined by the drift time of the charge carriers.

Assuming that these events occur at the boundary between the reference channel (channel 8) and an adjacent channel, they are identified as CS events. However, it is crucial to consider the shape of the signal at the output of the CSA, and particularly the RT value, to identify random coincidence events.

Therefore, we devised an algorithm for active collimation and recovery of CS events. Upon event detection, with the modalities described in Section III, the algorithm examines if another event occurs in a neighboring channel within a finite CW. The choice of the length of the CW follows the analysis presented in Fig. 11, employing similar criteria as those used for determining the maximum RT filter value (Fig. 10). An optimal CW for this measurement is found at 300 ns, as evident from these graphs: while the peak-to-tail ratio experiences an improvement of a factor of 2.7, the number of events in the Mn-K$\alpha $ peak does not vary significantly.

Fig. 11.

(a) Peak-to-tail ratio and (b) integral of the Mn-K$\alpha $ peak with respect to different values of the CW. The graphs indicate that the optimal CW for this measurement is at 300 ns. This is evident from the significant improvement in the peak-to-tail ratio by a factor of 2.7, while the peak integral already reaches its maximum at this point.

If no additional events in the CW are detected by neighboring anodes, the initial event is included in the spectrum.

If, however, a neighboring anode detects an event within the CW, the algorithm assesses the RT of both events to determine whether these events involve CS, signified by a longer RT, or if it is a random coincidence. When two events are identified as genuine CS events, their amplitudes are summed and incorporated into the spectrum, as illustrated in Fig. 9.

SECTION V. Results

The CS recovery algorithm was extensively tested and validated on an uncollimated 2-mm ARDESIA-16 detection module (Section II).

For an initial assessment of the effectiveness of our algorithm, we eliminated events identified as CS occurrences from the spectrum of our triggering channel, as depicted in Fig. 12. The removal process involved progressively eliminating events shared with an increasing number of channels, initially avoiding their addition to the final spectrum.

Fig. 12.

Progressive removal of shared events in the spectra of channel 8. Each step excludes events shared with an increasing number of channels, providing background reductions ranging from 15% to 25%. The contribution of channel 7, absent in the setup, was estimated, resulting in an overall background reduction of 80%. The inset shows a zoomed-in portion of the background, highlighting its reduction with each consequent step.

With the removal of each additional channel, there is a reduction in spectrum background ranging from 15% to 25%. Although channel 7 was not directly measured because of the limit on oscilloscope channels, its contribution to CS can be estimated. The overall background reduction is estimated to reach 80% when considering the influence of all four surrounding channels.

Our CS recovery algorithm operates in two sequential steps. First, we apply an active collimation filter on the spectrum, which discards events occurring within a 300 ns CW and exhibiting a RT longer than 200 ns (Section IV-A). This results in the red spectrum shown in Fig. 13.

Fig. 13.

Results of the CS recovery algorithm: in blue, the uncollimated spectrum of channel 8 is shown, including both single-pixel and CS events. After applying a CW of 300 ns and a RT threshold of 200 ns, the red spectrum is obtained, labeled as active collimation spectrum. Most CS events are filtered resulting in a reduced background. The yellow spectrum combines the amplitudes of events identified as CS across neighboring channels. The position of the peak of reconstructed CS events coincides with that of the peak of full-energy events, indicating that with the shaping time reported in Section III-C we expect to collect all the charge. With shorter shaping times, ballistic deficit might occur, necessitating separate energy calibration of both spectra. The final combined spectrum, depicted in purple, is the key result, obtained by merging the filtered events (red) with the recovered CS events (yellow). The inset displays a zoom on the Mn-K$\alpha $ peak, emphasizing its increase with the implementation of the summing algorithm.

Following this, the CS identification algorithm is applied, and events that are recognized as having undergone CS have their amplitudes summed. A histogram is then generated based on these summed amplitudes, resulting in the yellow spectrum of Fig. 13. As expected, this spectrum exhibits a peak at 5.898 keV, confirming the hypothesis that the summation of CS events can lead to their recovery as useful signals. Results are summarized in Table II.

TABLE II Effect of Different Collimation Techniques in Mn-K $\alpha $ Peak Counts and Peak-to-Tail Ratio

Upon merging the recovered events with those that were not initially filtered out, the final outcome of our algorithm is obtained and represented by the purple spectrum in Fig. 13. Remarkably, in our measurements, this combined spectrum maintains a background level comparable to that achieved with CS rejection, with an increase in the peak-to-tail ratio by a factor of 2.7, while exhibiting an 8% enhancement in the photopeak. This observation is especially interesting given that only 14% of events are estimated to be impacted by CS when no collimation is implemented, thus demonstrating that the aforementioned algorithm is capable of recovering approximately 60% of CS events.

While a mechanical collimator of 0.5mm side introduces physical shielding to 45% of the active area of the detector, thereby theoretically reducing peak events by 30% (considering that approximately only 14% of the shielded area is affected by the CS phenomenon), the recovery algorithm, even with only three neighboring channels, reconstructed 8% more peak events when compared to the uncollimated case, effectively retrieving information that would intrinsically be lost due to the effect of CS in monolithic SDD arrays.

Moreover, with the setup described in Section III, and particularly the acquisition performed using the four-channel oscilloscope, CS was evaluated between the reference channel and three surrounding channels only. We estimate the potential to increase the peak-to-tail ratio by a factor of 3.6, and to recover 11% of events with the measure of signals from all four surrounding channels (or eight, considering cornering channels), as indicated in Table II, suggesting the possible recovery of approximately 80% of all CS events.

The two methods can be combined (Fig. 14) by applying the traditional filter based on maximum RT exclusion to events that passed the CS filter, having longer RTs but not falling in a CW. This integrated approach aims to optimize the spectrum reconstruction by minimizing the background while adding information to the photopeak, ultimately enhancing the performance of active collimation.

Fig. 14.

Combined application of the two presented techniques for active collimation is illustrated. In blue, the baseline spectrum showing all detected events without collimation. After applying the RT filter with a 200 ns threshold, the green spectrum is obtained, significantly reducing the background. However, as shown in the inset, information in the photopeak is lost as some single-pixel events interacting in the channel diagonal are discarded. The purple spectrum shows the results of the CS recovery algorithm based on CW, as in Fig. 13. The orange spectrum exhibits the result of the integrated approach, that entails the application of the CS recovery algorithm followed by the maximum RT filter on events recognized as single-pixel, combining the benefits of both techniques.

Indeed, the implementation of both the CS recovery algorithm and the RT filter results in a 5% increase (estimated as 6% when considering the four channels adjacent to the reference pixel) in photopeak events compared to the scenario with no collimation. Simultaneously, the peak-to-tail ratio experiences a substantial improvement, increasing by a factor of 9.1 (estimated as 12 when considering the four adjacent channels). This dual collimation strategy demonstrates its effectiveness in optimizing the spectrum by enhancing photopeak events and significantly reducing the background continuum, thereby contributing to improved overall performance.

This enhancement significantly increases the detector efficiency beyond what would be achievable with other methods. Moreover, it surpasses the efficiency obtained without any collimation. Without our algorithm, CS events limit the effective active area to the unaffected 86% of the pixel. However, with our algorithm, the discarded event area is reduced, reclaiming up to 80% of the affected area, thereby extending the total active area to 97% of the pixel.

SECTION VI. Conclusion

Our work addresses the challenges associated with the CS phenomenon in monolithic arrays of SDDs.

We presented the characterization of CS effects in a monolithic 16-channel ARDESIA detection module, employing a pulsed laser system for a precise assessment of the CS region. The small spot size of the laser beam ensured accurate evaluation, and the manual translation stage facilitated a high-precision scan of the SDD surface. The results indicate a CS region extending approximately $\mathrm {75~\mu \text { m} }$ on each side of a pixel, equivalent to about 14% of the total pixel area. This finding underscores the significance of addressing CS with collimation to maximize detector efficiency.

Collimation is indeed a crucial technique for improving the performance of SDD-based spectroscopy detectors. While mechanical collimation causes an additional loss in active area by up to 30%, electronic collimation offers a promising alternative.

By leveraging filtering algorithms based on key parameters, such as signal RT and the detector’s timing capabilities, we propose an electronic collimation method that enhances the efficiency of SDD-based detectors. Our method aims to restore the total effective active area by leveraging filters based on the RT of the signal of interest, and on the timing capabilities of SDDs. Compared to the standard RT filter, which retains 98% of single-pixel events, our approach retains 100% of single-pixel events, and recovers 10% more peak events (estimated to reach 13% with four channels), significantly increasing peak counts in the spectrum. Furthermore, combining this approach with the RT-based filter achieves a remarkable improvement in the peak-to-tail ratio, crucial for accurate peak identification.

Additionally, we eliminate the need for a custom-made mechanical collimator, simplifying the fabrication and assembly process of the module. Furthermore, our method maximizes the active-to-total area ratio, restoring the lost portion of the detector that a mechanical collimator would shield.

Future work will involve refining the algorithm and extending its applicability to SDD arrays featuring a larger number of channels, of particular interest in the context of high-rate fluorescence spectroscopy.

ACKNOWLEDGMENT

The authors declare that they have no known conflicts of interest in terms of competing financial interests or personal relationships that could have an influence or are relevant to the work reported in this article. They would also like to thank Sergio Masci for the wire bonding of the detection modules, the Politecnico workshop for the production of mechanical parts, and Fondazione Bruno Kessler for the design and production of the SDDs.

NOTE

Open Access provided by 'Politecnico di Milano' within the CRUI CARE Agreement