2.1.

Optical Blocking Filter

Due to the design of the MPOs and lobster eye instruments, a straight-through solid angle is present for particle trajectories. Therefore, instruments using this type of optic may see a higher level of optical stray light or increased background, and additional optical blocking filters (OBFs) are thus required, possibly more than for previous X-ray instruments due to the much larger field of view. The OBF can either be affixed directly to the CCDs as is common in non-MPO designs or be deposited directly onto the MPOs. The OBF is adhered to the front surface of the MPO, facing the radiation source. Due to the necessity of the OBF when using this type of optic, this paper will also explore the effects of an aluminum OBF on doses by altering its placement within the instrument. An OBF deposited directly onto the detector surface, referred to as on-chip, has been compared with OBF placements on the front or back of the MPOs.

3.1.

Solar Energetic Particles

The Sun is also a large source of radiation that emits a steady stream of protons and electrons via the solar wind. The lower bound of the energy spectra is on the order of a few electron volts, which is much lower than other particle sources such as GCRs. For the lower energy domain of the solar particle spectra, minimal shielding will mitigate against it. However, the Sun can also emit higher energy particles with a high flux from coronal mass ejections (CMEs) and solar flares. These particles are referred to as solar energetic particles (SEPs), and the majority of these particles are protons. Due to their low energies, SEP trajectories can be altered by instrument optics systems such as MPOs and thus become focused and cause additional damage.

Because SEP events are probabilistic phenomena, they are difficult to model; thus, current models predict the flux with an associated confidence level to account for this probabilistic nature. The Emission of Solar Protons and Prediction of Solar particle Yields for Characterizing Integrated Circuits (ESP-PSYCHIC) model is recommended by the ECSS-E-ST-10-04C²⁸ standards, and this model will be used for sectoral analysis dose calculations in this paper. However, during the studies, it was identified that the ESP-PSYCHIC model has an issue with its low-energy spectrum. The predicted flux of the ESP-PSYCHIC model decreases with confidence level; this is shown in Fig. 2, with the key inflection point marked with a red-dotted line at 0.163 MeV/nucleon. The cause of the inflection was identified from the SPace ENVironment Information System (SPENVIS) documentation²⁹ and is due to the amalgamation of two separate models: ESP and PSYCHIC. These are coupled together using scaling factors, and the lower bound is at 0.173 MeV/nucleon, marked as a green line in the figure. Therefore, below 0.173 MeV/nucleon, the scaling factors may not alter predicted fluence. Figure 2 exhibits the evidence for this feature, and as the confidence level increases, the flux decreases below 0.163 MeV/nucleon. This will cause the dose from low-energy protons ($\lesssim 200\mathrm{keV}$) to be under-predicted for increasing confidence levels. This lower energy range is important as bulk damages to silicon detectors occur, and peak damage occurs around 100 keV.³⁰ Consequently, for regions with minimal aluminum equivalent thickness shielding, this will be an issue as the dose would likely be higher. Thus, this will affect the sectoral analysis approach for unfocused dose calculations that use depth dose curves from SPENVIS.

Fig. 2

ESP-PSYCHIC confidence level issue. The inflection point is marked with a red dashed line at 0.163. The green dashed line indicates the energy (0.173 MeV/nucleon) where the scale factors in the model start. Therefore, the model extrapolates for energies below this point. For the solar protons shown, the nucleon number is one.

The depth is defined from the outer surface inward to the center of the volume. Due to the inflection observed in the ESP-PSYCHIC model, experimental time-series data were used as an alternative representation of the SEP spectra. An Advanced Composition Explorer - Electron, Proton and Alpha Monitor (ACE-EPAM) dataset from 1997 to 2013 (ACE-EPAM data provided by Nicholas E. Thomas of the University of Maryland Baltimore) was used. The data for ACE-EPAM and ESP-PSYCHIC are compared in Fig. 3. The flux for the ESP-PSYCHIC models was calculated at 95% confidence and shows an agreement with the 95th percentile range of the ACE-EPAM time-series derived data as expected. Depth dose curves for the ACE-EPAM were produced using the SHIELDOSE-2 and non-ionizing energy loss for simple geometrical tools in SPENVIS. Both the ESP-PSYCHIC and ACE-EPAM dose contributions are compared for the SSA of the unfocused dose. For Monte Carlo simulations of the focused dose, only the ACE-EPAM time series is sampled and used to to seed all simulated particle spectra.

Fig. 3

Average flux measurements from a variety of models and datasets. The ACE-EPAM error bars represent the 5th and 95th percentile ranges. The ESP-PSYCHIC models were taken from SPENVIS estimates for highly elliptical orbital parameters similar to those planned for the SMILE mission.

4.1.

Segmented Technique

The segmented technique uses many justifiable approximations to create a simplified version of the lobster eye optic. The MPOs that form the lobster eye optics are approximated to be made of large area flat panels that form the curved surface in the $(\theta ,\varphi )$ axes, as shown in Fig. 5(a). Using equal angles in $\theta$ and $\varphi$ creates square segments. Due to the symmetries of the lobster eye over the detectors, only a quadrant of the optics is required to be simulated, as depicted in Fig. 5(b), reducing the CPU time required for the simulation by a factor of 4. A quadrant represents a $2\times 4$ MPO unit, whereas the whole SMILE SXI optic is formed of two $4\times 4$ MPO units.

Fig. 5

Segmented geometry simulation setup. The track color represents the charge of the particles. Positively charged particles, mainly protons with some positrons, are blue, and negatively charged particles, consisting primarily of electrons, are red. Green tracks represent photons and other neutral charge particles. Interactions between the particles and geometry are shown as yellow points.

Reflecting the data generated from the quadrant can be used to create a full-dose map across the focal plane. Data from the yellow segments require one reflection, whereas those in red are reflected multiple times to construct an image. However, to achieve unique variations in each quadrant, four simulations need to be combined. This removes patterns caused by mirroring the data to achieve a full-dose map. The MPO pores are simulated using the G4_GLASS_LEAD material in the Geant4 NIST compound database. It should be noted that the iridium coating was not included in these simulations to simplify the geometry.

To simplify the model, each simulated square MPO segment is flat, and the curvature comes from the rotation of each mirror segment unlike the flight MPOs, which will have an internal curvature. For a segment, it is assumed that the dose contribution and CCD interaction location from a particle traveling through a pore is the same for the whole segment. This approximation is made to reduce the complexity. Therefore, only a small array of the MPOs is simulated in the center of the segment, as shown in Fig. 5(c). This approximation has the added benefit of removing any potential edge effects from the flat segments overlapping to produce the MPO curvature. The size of the central MPO array can also be altered to improve the focus of the segment. The segmented simulations presented in this paper use a $9\times 9$ grid such that multiple scatters to the detector can be simulated, rather than a smaller $3\times 3$ grid, which could lead to a proportion of particles not being focused toward the focal plane.

Particles are generated over the central pore, including the pore wall, with a Lambertian angular distribution to replicate the isotropic radiation sources in space. The simulation is performed in the frame of reference of the central pore, with the CCDs being rotated between simulations to replicate data from different MPO segments. Only the MPOs and CCD geometry objects are simulated.

The energy deposits, interaction positions, and additional information are recorded from the CCD-sensitive detector objects. This is post-processed with multiple normalizations applied to account for the approximations and to enable dose rates to be calculated. The total non-ionizing dose was calculated from non-ionizing energy loss (NIEL) in the simulation. This was achieved by backporting the CalculateNIEL function from the Geant4 10.7 source code. This Geant4 function is limited and only works for protons and alpha particles that deposit energy.

4.2.

Full Pore Technique

The full pore method aims to simulate as many of the MPOs that form the lobster eye as possible for a more physically representative simulation. The geometry of each simulated MPO is built from many spherical segments and thus more accurately represents the mission-like MPOs. The MPO geometry of the full pore technique is shown in Fig. 6(a). Similar to the segmented method, G4_GLASS_LEAD is used for the MPOs, and the iridium coating was not included. Over $1.7\times {10}^7$ geometrical objects were created for the modeling of the SMILE SXI, which carries a computational overhead.

Fig. 6

Full pore detector construction geometry. The number of pores shown is reduced such that the visualization manager can display them on the screen. The low polygon count in the Geant4 visualization is not present in the simulation kernel, so there are no overlapping volumes. The particle generation direction samples from a cosine distribution that is used to replicate the isotropic distribution of particles in space. As shown in the image, some particles are directed away from the detector due to the curvature of the lobster eye optic. (a) Zoomed in view of MPOs. (b) Geantino particle generation tests.

The particles are generated on a segment of a sphere and once again sampled from a Lambertian distribution to replicate the isotropic nature of particles entering the MPOs. Figure 6(b) displays an example of the particle generation region’s validations using non-interacting special Geantino particles in Geant4. The particle generation region can be set to a quarter of the MPOs and uses symmetry approximations to reduce the CPU time, similar to the segmented technique.

Due to the simulation design modularity, additional masses can be added such as the optical blocking filter. In its default form, the simulation does not include additional masses and only includes aluminum and titanium base structures, with the glass MPOs and a silicon block representing the CCDs.

Similar to the previously described segmented technique, simulations of the energy deposits and interaction positions in the CCDs are recorded. The data is post-processed, and normalizations are applied where required. The post-processing stage is quicker in comparison with the segmented simulations as coordinate transformations are not required.

5.1.

Comparison of Models for Unfocused Dose

The SSA technique uses a depth dose curve from SPENVIS using a 95% confidence level. For the early spacecraft design concept phase for the SMILE mission, referred to as SXI 1.x, the unfocused radiation dose assessment that indicated the TID was 1.14 krad and TNID $2.3\times {10}^9{\mathrm{cm}}^{-2}$ for 10 MeV equivalent protons, using the SSA method, with the ESP-PSYCHIC model.

The values are calculated from two separate mass models: one with the SMILE radiation shutter door closed and one with it open. It is assumed that the door is closed when passing through the trapped particle regions. When the door is open, only the SEP dose is calculated. The total dose presented in the calculated values is calculated with summed weightings based on the expected door closure time. These predicted dose values do not include the impact of GCR and their resultant secondaries, and this is typical with SSA.

The ACE-EPAM data was also used to predict the SEP dose for the unfocused scenario. The input spectra have a maximum input energy of 4.75 MeV. The dose estimate using ACE-EPAM-based depth dose curves returned zero doses for both open and closed models. This is because the energies and associated particle fluences were not high enough. The ESP-PSYCHIC was also cut down to a 4.75 MeV maximum energy and returned a zero dose, validating the energy relation (Table 3).

Table 3

These focused datasets use the ACE EPAM 2013 time series as input for SEP modeling, and their errors are based on simulation statistical results. The dose estimates are for a 3-year mission of SMILE SXI 1.x.

5.2.

Comparison of Focused Dose Techniques

The two focused dose techniques were used to calculate the dose for a lobster eye optic using the parameters listed in Table 1. The errors are based on the simulation statistics used. They do not include approximation or systematic uncertainties. In the absence of experimental data for validation, the data does reveal the same order of magnitude that is observed for the two techniques.

The segmented simulation is faster than the full pore simulation; however, it requires post-processing to perform coordinate transforms. The total time of simulation and analysis for the segmented technique is longer than that of the full pore technique. Code optimization of the post-processing would likely make the segmented technique quicker overall. Therefore, for larger MPO structures, this presents an alternative approach with a reduced simulation time and resource complexity.

5.3.

Focused Versus Unfocused Dose

The unfocused results, which use the ESP-PSYCHIC SEP model, are used for comparison in Sec 5.3 despite the issues already identified with the confidence levels with the model. The reason for this choice is that it is more representative of the full-duration mission. That includes periods of increased SEP rates from solar activity and has a wider energy range. This leads to unfocused dose predictions that are non-zero. The ACE-EPAM data are being used for the focus as they are more representative of the day-to-day SEP rates. When the SEP rate is up, the radiation shutter door will be closed to protect the CCDs, and the focused dose component will be mitigated against.

The results show that the focused dose corresponds to $\sim 15\%$ of the combined focused and unfocused dose components for the TID, and the focused dose represents the TNID $\sim 63\%$ of the combined dose. Therefore, this highlights the importance of considering both the focused and unfocused doses for missions that include lobster eye MPO X-ray optics. Breaking down the unfocused TID into components shows that the SEPs contribute 0.898 krad and 90% comes from the open-door position. The same is observed for TNID. The dose contribution from low-energy particles is missed by the SSA unfocused calculations, due to the dose depth curves as previously demonstrated.

For the SMILE SXI version 1.x design, parameters and radiation environment were used to create the data for the unfocused and focused doses. The CCDs would be below the dose limits for a 3-year mission. However, increases to 5 years and beyond would not be advisable when including the focused dose. Thus, this shows the importance of including the focused dose component in which the instrument operation for science returns is dependent on dose. If the focused optical estimates are accurate, then nearly two-thirds ($\sim 63\%$) of the TNID dose arrives via the MPOs. This further highlights the importance of considering the focused dose component for instrumentation that incorporates MPOs.

5.4.

Focused Dose Distribution

Both simulation techniques enabled the dose to be mapped across the CCD area. The two-dose maps for TID are shown in Fig. 7. The data show that the segmented technique produces a mostly uniform dose with the dose decreasing around the outer edges of the CCDs. By design, the segmented technique only simulated a few locations, which contributes to the uniformity. By contrast, the full pore produces a uniform dose with more noise across the device with an “$\infty$” pattern subtly observable in the data. The greater noise can be partly attributed to lower simulation statistics.

Fig. 7

Segment and full pore simulation TID positional map comparisons. The segmented technique was simulated with more data, and hence, the data is less noisy.

The full pore method was simulated twice with different particle generation regions: once with the full lobster eye optic area, representing the two $4\times 4$ MPO units and once for a quarter representing $2\times 4$ MPO units. The same “$\infty$” pattern was observed in both simulations and in repeats of the simulations. Therefore, this pattern is not an artifact resulting from only simulating a quarter of the full optic area. Geometry of overlap checks was performed in Geant4, which ruled out a geometry error causing the artifact. Therefore, it is suspected that the “$\infty$” pattern is due to the focusing of the simulated particles. The central ellipse was more circular when the MPO material was changed from lead glass to silicon during an investigation study. The patterns have also been observed to alter with changes to the radius of curvature of the lobster eye optic and changes in the MPO properties: pore width, wall width, and pore length.

The dose maps for the full pore method were analyzed at different depth cuts, where the depth is defined from the top surface of the device, i.e., the entrance window of the sensor. These are shown in Fig. 8. The cuts show the patterns and reveal that they become less refined the deeper into the CCDs the cuts are performed.

Fig. 8

Depth profiles of TID of full pore simulation. The four quadrants are marked to show the rough reflection points for the singular dataset.

Understanding the dose depth profile is crucial for devices such as CCDs, particularly in relation to the depth at which charge is stored and transferred within the devices. A key metric of CCDs, charge transfer inefficiency, is significantly degraded by charge trapping as a result of TNID. Therefore, the dose depth profile, and hence the level of charge trapping within the CCD buried channel, is key to accurately determining the effect on the CCD performance. The buried channel is located toward the bottom surface of the device.

The dose map depth cuts demonstrated that the dose reduces the deeper into the silicon the cuts are made. Figure 9 shows the plots for both TID and TNID with depth through the CCDs. The plots also compare the segmented and full pore simulations, with the two techniques showing good agreement with the distribution of doses. The top surface of the CCDs experiences the highest TID. This is where many low-energy particles are absorbed into the silicon. The dose drops below 0.2 krad at depths of $5\mu \mathrm{m}$ and below. Therefore, ionizing dose damage effects are most likely to cause issues at the top of the detector silicon. The buried channel is near the bottom of the device, and the damage occurs near the top. Therefore, due to the damage proximity from the buried channel, it leads to less of an operational impact than if it occurred deeper into the detector’s silicon.

Fig. 9

Depth dose comparison between the two simulations. The left side shows the agreement for the TID. The right side shows the TNID. It should be noted that the upper and lower bins of the TNID data are not included in the data presented due to a boundary problem in the TNID calculation used.

By contrast, the TNID is highest at a subsurface depth of $0.8\mu \mathrm{m}$. The heavier particles attributed with TNID have to travel a distance into the material before they are attenuated. The majority of the particles contributing to the TNID are from the SEP protons, rather than their secondary particles. It should be noted that the two surface bins were removed from the TNID plot as these have extremely high doses that are attributed to a boundary problem in the simulation, which is not physical.

The dose depth profiles demonstrate that different degradations of the sensor could occur depending on whether a front- or back-illuminated device is used. Detailed modeling of the operation of CCD or CMOS devices with the energy deposits would determine the specific impact.

5.5.

Optical Blocking Filter Configurations

The impact of the MPO OBF location on the TNID and TID was investigated. An aluminum OBF with a 100 nm thickness was simulated in three locations: on-chip (CCD), on the rear surface of the MPOs, and on the front surface of the MPOs (standard position). For the MPO OBF, the front surface is defined as the side of the MPOs facing the sky, and the rear surface is the side of the MPOs facing the detector.

Table 4 compares the TID and TNID between each setup. The simulation configuration without an OBF is used for comparison. All scenarios have a small reduction in dose from the simulated low-energy protons. When the OBF is on the front surface of the MPOs, the TID is the highest of all three OBF scenarios tested, and the results are the closest to without an OBF. Any particles generated from the front surface OBF will also be focused down, through the pores, onto the CCDs. The OBF on the rear surface of the MPOs was used to test this theory, in which any scattered particles from the OBF are not focused down toward the detector. This causes this OBF configuration to have the lowest TID and TNID. However, it should be noted that it is not currently mechanically feasible to affix the OBF to the rear side of the MPOs.

Table 4

Total ionizing dose and total non-ionizing dose for different optical blocking filter configurations using the geometry method simulation. The error on the TID values is ∼1×10−4  krad. The TNID has errors with an order of magnitude of ×107  cm−2.

The on-chip configuration has the highest TNID of all three simulations. The higher dose is attributed to the production of low-energy secondaries produced from primary interactions with the OBF. Due to the particle species and energies of scattered lower energy secondaries produced, they are absorbed into the device increasing the TNID. Given the impact of dose on the operation of the CCD detectors for a mission such as SMILE, the TNID is more of a concern. Therefore, minimizing the TNID is key for increasing their operational lifetime, ruling out the on-chip OBF with the current thickness for the tested configuration. A thicker on-chip OBF could potentially reduce the TNID in this scenario. Thus, simulations would be required for the specific mission and OBF configuration used.

Placing the OBF on the MPO’s front surface offers the best scenario given the manufacturing difficulties of an OBF on the rear surface of the MPO. Both MPO-based OBF configurations have the benefit that the MPOs act as another shield for the lower energy particles to be absorbed. A thicker OBF will also likely further reduce the TID result.