Cosmic-Ray-Related Signals from Detectors in Space: the Spitzer/IRAC Si:As IBC Devices

The Si:As IBC detector arrays in IRAC have a format of $256\times 256$ pixels with each pixel of dimensions $30\times 30$ $\mu$m, under which is an infrared-active layer $25$ $\mu$m thick followed by a $4$ $\mu$m thick blocking layer followed by the output electrical contact. This structure is back-illuminated through a $\sim$ 500 $\mu$m thick substrate with a buried electrical contact between the substrate and IR-active layer.

We retrieved both Level 1 and Level 2 data products obtained with the IRAC arrays from the Spitzer Heritage Archive¹¹1http://sha.ipac.caltech.edu. The Level 1 products contain Basic Calibrated Data (BCD) files, which are individual exposures that have not been corrected for outlier rejection. The Level 2 products contain the mosaic files (*maic.fits), which were resampled, and weighted images derived from the BCDs excluding outlier-affected pixels. Figure 1 shows an example of a mosaic image (top), and the coverage of the BCD files (bottom) that were used to make the mosaic image.

Table 1 summarizes the data used for this study. PIDs 169 and 194 (GOODS North and South) are ideal because they provide long, uninterrupted exposures in low background regions. Figure 2 plots the spacecraft position in distance from the Sun and Earth as a function of observation date. Even by the first epoch, the spacecraft is well beyond the distance of the L2 Lagrange point ($\sim$ 0.01 AU from Earth), and beyond any shielding effects from Earth’s magnetosphere. The primary shielding is thus provided by the spacecraft and instrument structure. An aluminum thickness of 4 mm is sufficient to block nearly all of the proton flux (i.e., protons $<$ 20 MeV) from the quiescent sun. However, coronal mass ejections accelerate protons into the hundreds of MeV range (e.g., Bruno et al., 2019), and during these events the Solar proton flux can penetrate the shielding to dominate the flux received at the detectors. Figure 3 shows the time periods of our analysis compared with the measured overall proton flux (the details of the flux derivation are provided in Appendix A). Our analysis focuses on quiet periods, and hence the proton events are dominated by GCRs, the flux of which varies in anti-synchronism with the solar cycle (i.e., is lowest near solar max). .

Comparison with data from ground test of the Mid-Infrared Instrument (MIRI) for JWST can provide a useful perspective. The baseline MIRI detector arrays are similar to the IRAC arrays except they are $1024\times 1024$ pixels in format and each pixel is $25\times 25$ $\mu$m, with an IR-active layer $35\mu$m thick. On the ground, cosmic ray hits on a detector array are dominated by energetic muons, because these particles penetrate the atmosphere. Thus, these events show the effects of hits by particles exclusively with a single atomic charge. This can be compared directly with results for the IRAC arrays in space, because the MIRI Si:As IBC detectors are very similar to those in IRAC (they have a much larger format, but otherwise with 20% smaller pixels but a 40% thicker IR-active layer, the pixel areas (which are of primary interest for this study) are virtually identical) (Ressler et al., 2008; Rieke et al., 2015). Data for these arrays were obtained from the third instrument cryogenic-vacuum instrument testing (CV3).

To identify and measure CR hits, we perform the same analysis on all of the IRAC data. Each BCD file has a corresponding Rmask file (*brmsk.fits) that flags outlier pixels. For our datasets, the Rmasks were all generated with box outlier rejection where an outlier pixel was marked with a bit 3 value, or value = 8, as described in the MOPEX User Guide (Makovoz et al., 2012). The examined data sets had robust outlier rejection for each BCD, since there was sufficient coverage to support this process. To obtain reliable results for this work, we inspect the individual Rmask files to exclude poor and/or unreliable masks. For example, we ignore noisy columns and rows along the array edges (following Hora et al. (2006)). Specifically, we examine a 246x246 area on the array, ignoring the first and last 5 rows and columns of the detector.

Next, we resample the BCD and mosaic files so that they have the same pixel size to allow for direct flux comparisons. To remove the background in each field, the median value of each BCD and mosaic image is subtracted from the image itself (we will refer to this as the “leveled BCD image” and “leveled mosaic region,” respectively). The pixel values of CR hits identified in the Rmasks are first measured in the individual “leveled BCD images.” To remove any real flux from underlying astronomical features, we then subtract the corresponding values (same point in the sky) in the “leveled mosaic region”, which have had any potential CR contributions removed in the mosaic and stacking process. The resulting values are the measured intensities of the radiation hits used throughout this paper. Ultimately, only 16 Rmasks were rejected from the Channel 3 data set, and 3 Rmasks were rejected from the Channel 4 data set. The total number of BCDs analyzed is 8509 and 34094 for Channels 3 and 4, respectively.

The MIRI data, full-frame readouts in FAST mode, were reduced through a standard pipeline to produce smooth, unstructured images. We then identified “jumps” at a threshold of ten standard deviations above the noise level for a pixel.²²2https://jwst-pipeline.readthedocs.io/en/latest/jwst/jump/description.html##algorithm To eliminate instances where these jumps might not be cosmic ray hits, we rejected pixels with elevated noise levels, including: (1) cases identified in the first three reads of an integration ramp, when the MIRI arrays are recovering from the reset; (2) instances occurring within 10 pixels of the edge of the array; and (3) any jumps in the vicinity of regions of bad pixels (high dark current, excess noise etc.). The amplitude of the accepted jumps was determined by fitting straight lines to the signal prior to and after the cosmic ray event. The size of the event was measured by counting the affected pixels (with jumps similarly identified) within a $51\times 51$ pixel box.

Table 2 lists, and Figure 4 shows, the individual pixel hit rates versus time. There is a slow increase in the hit rate over the duration of the IRAC observations. This behavior is expected, because the level of Solar activity was changing (e.g., Ross & Chaplin, 2019), and reflects the resulting increase in proton flux as shown in Figure 3. Additionally, based on Figures 2 and 4, we do not find a correlation between the hit rate and location of the Spitzer spacecraft relative to the Earth and Sun.

The scatter in the hit rate is large, significantly greater than would result if the hits were from independent events. Furthermore, the rates are substantially larger in Channel 3 than Channel 4 (5.23 pixels/second versus 4.32 pixels per second, respectively). The difference presumably reflects differences in the degree of shielding and showering³³3Created from knock-on electrons, or “delta rays,” resulting from transfer of energy from a high-energy cosmic ray to electrons through interactions either with the detector material or that surrounding the detector. for the two detector arrays.

The observed hit rates can be compared with the predicted hit rates from proton fluxes, particularly since the shielding of the detectors reduces the contribution of solar protons to far below that of the GCRs. Since the GCR energy spectrum extends to very high energies, the dependence of the predicted hit rates from them is only very weakly dependent on the details of the shielding.

The proton fluxes plotted in Figure 3 are isotropic, i.e., integrated over 4 $\pi$ ster. To determine the expected hit rate from the GCRs, we convert to the intensity per unit solid angle, F(GCR)/4$\pi$. Each face of a pixel will receive hits over the equivalent of $\pi$ ster. The surface area of an IRAC pixel is $5.28\times 10^{-5}$ cm². We focus on a 246 $\times$ 246 pixel area of the array and compute hit rates for each of the five intervals where we analyzed the data; the lack of significant variations in the rates across each of these intervals suggests that we can ignore any time variability. The predicted hit rates are shown in Figure 4 as black dots across the bottom panel; the same predictions would hold for Channel 3 in the upper panel because the pixels are identical in size. It is obvious that the observed rates exceed the predictions substantially, by a factor of $\sim$ 2.7 for Channel 3 and $\sim$ 2.3 for Channel 4.

Figure 5 shows the hit amplitude distribution for both the Channel 3 and 4 IRAC arrays. Figure 6 plots the hit rate versus the hit amplitude. Figure 5 also includes data for the ISO Short Wavelength Spectrometer (SWS) Si:As IBC array, which were obtained from the “SWS Glitch Tables⁴⁴4Obtained from http://sws.ster.kuleuven.ac.be/__;!!CrWY41Z8OgsX0i-WU-0LuAcUu2o!msqEZ3a8CtO0fNMN1xKOg5zexH3iwBjni1eKFTg_9yiJ6bro6i1wfG3G1nEE2g” which is no longer active.,” and for a MIRI array obtained during cryo-vacuum test of that instrument. The IRAC detectors have an infrared-active layer that is 25 $\mu$m thick (W. Glaccum, private communication), and a blocking layer about 4 $\mu$m thick. We could not locate the corresponding parameters for the SWS detector, but based on the time of manufacturing, the IR active layer would be about 20 $\mu$m thick (these devices were less developed than the IRAC detectors, but had similar architecture). The IR-active layer in the MIRI array is 35 $\mu$m thick. Assuming that free electrons are collected from just the IR active plus the blocking layers, the relevant detector thicknesses are $\sim$ 24, 29, and 39 µm for the SWS, IRAC, and MIRI detectors, respectively.

A cosmic ray with a single atomic charge and at the minimum ionizing energy, at normal incidence onto a detector, will produce on average $\sim$ 3000 free electrons in the 29 $\mu$m thick infrared-active plus blocking layers of each of the IRAC arrays (assuming the energy loss to be the minimum, namely 1.66 Mev g^-1 cm^-2 and the average energy required to free an electron to be 3.6 eV). We describe this as the minimum average ionizing yield. This region shows as a “bump” on the yield curves, particularly that for Channel 3. The drop of the yields above this region demonstrates that the buried contact, which separates the $\sim$ 500 $\mu$m thick substrate from the IR active layer, is an impermeable barrier for free electrons produced by cosmic ray ionization in the detector substrate.

To understand the full behavior, it is useful to start with the MIRI detector, where virtually all the hits are from muons, i.e. have single atomic charge. In this case, the behavior should be as described by the Landau Distribution; the curve in Figure 5 is the combination of two such distributions for minimum average ionizing particles, one for normal incidence and the other for incidence 45^o off normal. Hits with electron yields above the muon/Landau behavior towards the right of Figure 5 are likely to be dominated by particles with multiple atomic charges, e.g., alpha particles (ionization loss goes as atomic number squared). The three sets of data obtained in space (i.e., for the ISO and IRAC arrays), where the detectors are exposed to the full set of cosmic ray particles, all show substantially more events above the range than can be attributed to high-energy single-charge particles striking the detector array.

The excess of hits below the minimum average ionizing particle yield (towards the left of Figure 5) has also been observed for the HST NICMOS HgCdTe arrays (Ladbury et al., 2002)) and the Gaia CCDs (Crowley et al., 2016). To first order, this behavior is due to the statistical nature of ionization loss by an energetic particle, which proceeds by discrete interactions and hence is subject to statistical fluctuations. In typical range calculations (e.g., for shielding), there are so many interactions that the statistics average out to a well determined value (e.g., Glasse et al., 2020). However, the loss in the thin layers in detectors involves a small number of interactions and the range of losses is significant. This effect is frequently overlooked, but, for example, the library of simulated cosmic ray hits provided by Robberto (2010) includes the statistical distribution of hit sizes correctly, and the behavior is also shown in Physicist (2021).

That the statistical effects are the primary source of the lack of an inflection in the hit spectrum indicative of the minimum ionizing yield is clearly demonstrated by the analysis in Garcia et al. (2018) for the Gaia CCDs. Their initial simple analytical model, which had an overly simplistic energy deposition description, was insufficient. Instead, they carried out a Monte-Carlo simulation using the Geant4-based tool GRAS7, which is designed for radiation analysis for space. The simulation included the detectors as well as the surrounding spacecraft. The investigation also: (1) verified that protons are the dominant source of hits; and (2) and included a more complete and accurate set of energy deposition processes. The starting point for the simulation was the CREME96 cosmic ray spectrum, but the nominal shielding of the CCDs was not included since the spacecraft serves that purpose. The more complex model confirmed that the distribution of free electron yields from cosmic ray hits on the CCDs was generally well-reproduced when the statistics of the ionization process were included.

A small number of very small hits persist above the predictions from the analysis of Garcia et al. (2018) (see also Mouri et al. (2011) for evidence of such behavior in Si:As IBC detectors similar to the IRAC ones). These small hits might originate from a weakly ionizing target (i.e., the array multiplexer rather than the detectors). Alternatively, they may be unrelated to cosmic ray hits, but instead arise in momentary breakdown in high-field regions of the detector contacts (Rieke, 2002) or through other detector-related phenomena.

An important aspect of the simulated events by Robberto (2010) and the modeling by Garcia et al. (2018) is that the apparent turnover in the numbers toward very small hits in Figure 5 is real – the hit size spectrum does not continue to grow toward smaller and smaller hits. Figure 6 highlights this point. Channel 3 has very few hits below $\sim$ 200 electrons; Channel 4 has a secondary small knee in this region, but it may be a detector artifact (spontaneous spiking) rather than a result of cosmic ray hits (as discussed in Section 5.1). In any case, the vast majority of cosmic ray hits are large enough to be easily identified with modern detector arrays that have read noises of 30 electrons or less.

The Spitzer Earth-trailing orbit kept the IRAC detectors away from sustained high hit rates. However, the Akari observatory in an Earth-centered, polar orbit passed through the South Atlantic Anomaly (SAA) three or four times a day, where its virtually identical Si:As IBC detectors were exposed to rates orders of magnitude greater than the quiescent GCR rate (Mouri et al., 2011). Under these conditions, the overall dark current from the entire detector array was elevated substantially (Mouri et al., 2011), but it recovered to nominal values soon after the detectors were no longer in the region of intense radiation, i.e., the SAA.

Next we consider the size of each potential radiation hit by counting the number of flagged pixels that are in an isolated group in the Rmask image. Such groups are defined as a set of interconnected flagged pixels that do not connect to another similar set. Figure 7 shows the size distribution of the radiation hits in number of pixels. The median size of the radiation hits in both Channels is 2 pixels. Other than the single pixel hits, the pixel size profiles appear to be similar between Channel 3 and Channel 4, though overall they are slightly larger in Channel 3. This may be because Channel 3 is operated at a lower bias voltage than Channel 4, which leads to increased charge spreading (Patten et al., 2004).

Figure 8 shows the results of a Monte Carlo calculation that simulates cosmic rays hitting and exiting a detector that contains pixels with same pixel physical dimensions as the IRAC pixels. This calculation gives a theoretical size profile of hits from cosmic rays incident at all angles that enter and leave an IRAC detector. The simulation assumes no charge spreading. Each simulated cosmic ray starts at a random, normalized $(x,y)$ location $(0\leq x\leq 1,0\leq y\leq 1)$ on the pixel surface with $z$ = $0$ and random $(\theta,\phi)$ angles $(0\leq\theta\leq\pi,0\leq\phi\leq 2\pi)$ to describe an angle of incidence from the isotropic flux of incoming cosmic rays. Using the equation for a line in 3D space, we determine the location when the simulated cosmic ray leaves the detector. From here, we calculate the number of pixels the line has passed through from its start and end points.

Figure 8 compares the results from the Monte Carlo simulation with the actual data. To first order, the simulations and the data behave similarly. The most prominent discrepancy is the larger fraction of observed single-pixel hits in Channel 4 compared with predictions. This behavior is consistent with the possibility that some of these “hits” result from spiking in the detectors or readouts, since those events would affect single pixels only. Otherwise, the deviations of the simulation from the observed behavior appear to be in opposite directions for the two channels, i.e., an excess in the real data for Channel 3 and a deficiency for the simulation in Channel 4. However, if we assume that the single-hit count is artificially amplified in Channel 4 and redistribute the excess above the single-pixel Monte Carlo prediction into the other bins, the Channel 4 numbers exceed the Monte Carlo result just as for Channel 3. This excess above the Monte Carlo simulations probably results from: (1) scattering and showering of particles within the array or close to it (Patten et al., 2004); (2) an energetic particle launching ionization products with significant energy and their ability as a result to migrate farther than the diffusion length (Han & Guo, 2017); and (3) crosstalk due to interpixel capacitance.

We now re-examine the hit rate vs time for the isolated radiation hits. While Figure 4 plots the hit rate assuming all pixels are independent, Figure 9 plots the hit rate assuming an isolated group is a single hit. In this case, the hit rate is now lower in Channel 3 than in Channel 4, which is expected because the size (in pixels) of the radiation hits in Channel 3 is larger than the radiation hits in Channel 4. We still see a trend where the hit rate increases with time.

We next perform a similar analysis with the amplitude distributions of the isolated groups to probe the entire yields from a cosmic ray hit. Figure 10 plots the intensity for each group summed over all the pixels. Figure 11 normalizes these numbers dividing by the number of pixels in the group. In Figure 10 the intensity profiles are similar for hits with higher intensity. The Channel 4 data contain more hits of lower intensity, and vary significantly in the different observation periods. This variation is due to hits that are one pixel in size, as previously noted in Figure 8. When we normalize the intensity of a group by the number of pixels in the group, the intensity profiles are similar overall. Like Figure 6, Figures 12 and 13 plot the hit rate versus the hit amplitude, but for the groups of pixels. The shape of these profiles is similar to the intensity profiles found in Figures 10 and 11.

Finally, we compare the intensity distributions for different group sizes across the five observation periods (Figures 14 and 15). The intensity profiles do not change significantly between observation periods, with the exception of the single pixels in Channel 4. This lack of variations reflects both the relatively weak diagnostics of the GCR spectrum through these intensity profiles, and that the GCR spectrum does not change dramatically with time in the relevant 30 - 300 MeV range (e.g., Buchvarova & Velinov, 2010). For single-pixel events in channel 4, “Observation Period 4” (shown in purple) has the strongest first mode, while “Observation Period 1” (shown in blue) has the weakest bimodal behavior. This difference in the face of the lack of any other differences supports the suspicion of a weakly unstable spiking behavior contributing single-pixel counts in this channel.

Figure 16 plots the values of the adjacent and diagonal pixel hit intensity relative to that of the central pixel. The average value for adjacent pixels is approximately 4.3% of the average for the hit pixel, whereas the diagonal pixels received only 0.7%. These values are comparable for hits regardless of intensity. All together, this result is indicative of some form of crosstalk. We note, however, that most of these adjacent pixels are not flagged as outliers because they are below the threshold for identification as separate hits.

There are two plausible mechanisms for crosstalk: (1) distribution of free charge carriers from one pixel to another; and (2) interpixel capacitance, IPC; (e.g., Finger et al., 2005; Fox et al., 2008; Rauscher et al., 2007). Models of these detectors indicate that the diffusion length is $\sim$ 2.5 $\mu$m (Rieke et al., 2015), which applies to thermalized free electrons. In addition, ionization by protons of $\geq$ 100 MeV can produce super-thermal free electrons that migrate much further, e.g., to 10 $\mu$m (e.g., Han & Guo, 2017). Crosstalk by motions of free electrons will be a statistical process. In comparison, interpixel capacitance IPC), unavoidable between the members of the grid of detector contacts, should be a purely electrical phenomenon and should not depend on the type of particle producing the hit (e.g., proton or electron or muon), or its hit position within a pixel.

IPC is a cause of crosstalk for all infrared arrays, but we need to determine whether motion of free electrons also contributes. To do this, we identified cases of muon hits on a MIRI detector array isolated to a single pixel. To remove instances where the muon had passed through a small portion of a second pixel, we rejected the adjacent pixel with the largest effect from the hit. Using the three remaining adjacent pixels we compared the mean frame differences to the frame differences of the pixel with the muon hit. A low level of crosstalk (Dcross $\sim 3.06\pm 0.66$%) was found for pixels adjacent to one hit by a muon, consistent with the results for the IRAC detectors given the somewhat different detector architectures. However, there was substantial rms scatter (more than 20% of the average value), inconsistent with the deterministic nature of IPC-driven crosstalk. We conclude that, on top of the crosstalk due to IPC, there is a significant contribution from thermal and/or super-thermal electrons migrating between pixels.

Figure 17 shows the hit rates, parameterized as the fraction of the total number of pixels that are flagged as outliers as a function of time. After adding pixels affected by crosstalk rather than being hit directly, the number of pixels affected by a hit increases over the single-pixel estimates by more than a factor of three in both IRAC Channels. The hit rate itself would have a linear dependence as shown for the shorter time intervals, e.g., $\sim$ 7.5% of the pixels hit in 1000 seconds. The nonlinearity for longer times results, however, because already-hit pixels are not flagged when they are hit again.