Skipper-CCD Sensors for the Oscura Experiment: Requirements and Preliminary Tests

The Oscura detector is a 10 kg silicon skipper-CCD array. To comply with standard fabrication processes, each sensor has 15 $\mu$m $\times$ 15 $\mu$m pixels and the standard thickness of 200 mm silicon wafers (725 $\mu$m). With these pixel dimensions, Oscura will need a 26 gigapixel array to achieve 10 kg of active mass.

The whole detector design and shielding are based on the constraints for reaching the Oscura background goal. The instrumental background restricts the sensors’ performance parameters, and it will be deeply discussed in Section 2. For the radiation background, Oscura plans to reach 0.01 dru, which corresponds to a significant improvement over previous CCD experiments [35, 36, 14, 37]. This mandates strict control of all materials selected for the experiment and imposes a cosmogenic activation control requirement, particularly significant for the sensors (less than five days of sea level exposure equivalent after tritium removal [38]).

The Oscura design is based on 1.35 Mpix sensors ($1278\times 1058$ pixels) packaged on a Multi-Chip-Module (MCM), see Fig. 2 (left). Each MCM consists of 16 sensors epoxied to a 150 mm diameter silicon wafer, with traces connecting the sensors to a low-radiation background flex cable [39, 40]. MCMs will be integrated into Super Modules (SMs), where each SM will hold 16 MCMs using a support and shielding structure of custom ultrapure electro-deposited copper [41], see Fig. 2 (center). The Oscura experiment needs $\sim$80 SMs to reach 10 kg of active mass. The full detector payload consists of 96 SMs, assuming a yield above 80%, surrounded by an internal copper and lead shield, arranged in six columnar slices forming a cylinder, see Fig. 2 (right).

“Dark current," i.e., thermal fluctuations of electrons from the valence to the conduction band, presents an irreducible source of 1$e^{-}$ events in skipper-CCDs. Operating the sensors with a low dark current requires cooling down the system to between 120K and 140K (the optimal operating point will be determined from the prototype sensors). The current strategy for the cooling system is to submerge the full detector array in a Liquid Nitrogen (LN2) bath operated with a vapor pressure of 450 psi to reach this temperature. Closed-cycle cryocoolers will provide the full system cooling capacity (less than 1 kW power) [42]. A schematic of the pressure vessel and its radiation shield is shown in Fig. 3.

Thermal dark current is an irreducible source of 1$e^{-}$ events in skipper-CCDs and constrains the lowest 1$e^{-}$ rate ($R_{1e^{-}}$) that can be achieved by Oscura. The 1$e^{-}$ events coming from dark current will generate pixels with 2$e^{-}$ or more by accidental coincidences. The count of $ne^{-}$ single pixel events for the 30 kg-year Oscura exposure can be calculated assuming a Poisson distribution,

where $N_{exp}$ is the total number of exposures per day, $N_{pix}$ is the total number of pixels in Oscura, and we assume a 3-year data-taking run. Here, $\lambda=R_{DC,1e^{-}}/N_{exp}$, where $R_{DC,1e^{-}}$ is the mean 1$e^{-}$ rate coming from dark current in units of $e^{-}$/pix/day. In Table 1 we present $K_{n}$ for different running conditions defined by $R_{DC,1e^{-}}$ and $N_{exp}$.

Table 1 shows that, in order to avoid accidental coincidences, it is better to have more exposures per day (large $N_{exp}$). The lowest $R_{1e^{-}}$ achieved in skipper-CCD detectors, reported by SENSEI [15], is $1.6\times 10^{-4}$ $e^{-}$/pix/day. Assuming we achieve this rate and considering dark current as its origin, we will have less than one accidental 3$e^{-}$ events, achieving the Oscura background requirement, if we operate with 2-hour exposures, i.e. $N_{exp}=12$ exposures/day. The Oscura sensors would still comply with the requirement with SENSEI’s $R_{1e^{-}}$ using 5-hour exposures. Table 1 also indicates that we need to improve the SENSEI rate by at least two orders of magnitude and read out the full detector in less than 2 hours to have less than one accidental coincidences of 2$e^{-}$ in one pixel, the Oscura background goal.

The Oscura CCDs are sensors with 1.35 Mpix. This means that, for each CCD, we need a readout rate higher than 188 (76) pix/s to reach Oscura background goal (requirement). As we plan to read each sensor with a single amplifier, the pixel readout time should be less than 5.3 (13.1) ms.

The readout noise and the threshold used to determine if a pixel has $ne^{-}$ define the number of $(n-1)e^{-}$ single pixel events that fall above the threshold to be counted as $ne^{-}$ events. In principle, a skipper-CCD’s readout noise can be made extremely small when multiple skipper samples ($N_{skp}$) are collected, as it drops as $1/\sqrt{N_{skp}}$ [12]. However, adding skipper samples makes the readout slower and, as shown in Table 1, longer readout times produce more accidental $ne^{-}$ events. An optimization between the readout noise and speed should then be considered when choosing $N_{skp}$.

The total count of $(n-1)e^{-}$ single pixel events counted as $ne^{-}$ events comes from integrating the tail of the $(n-1)e^{-}$ single pixel event normal distribution from the threshold for counting $ne^{-}$ events. It is given by

where $K_{(n-1)}$ is the total number of $(n-1)e^{-}$ single pixel events (see Eq. (2.1)), $\operatorname{erf}$ is the error function, $\sigma_{noise}$ is the electronic readout noise in units of electrons, and $(n-1)+e_{th}$ is the threshold used to determine if a pixel has $ne^{-}$. For example, for $n=2$, $e_{th}=0.5$, if the threshold is set to 1.5$e^{-}$.

From Eq. (2.2) we see that if $R_{DC,1e^{-}}=1\times 10^{-6}\,(1.6\times 10^{-4})$ $e^{-}$/pix/day, we need $e_{th}/\sigma_{noise}>5.4\,(4)$ in order to get $L_{2\,(3)}<1$, consistent with the Oscura background goal (requirement). As the noise increases, we need to increase $e_{th}$ to keep $L_{n}<1$, but higher values of $e_{th}$ produce inefficiency for counting $ne^{-}$ single pixel events. In fact, the efficiency (eff) is the integral of the $ne^{-}$ single pixel event normal distribution from the given threshold, and can be calculated as

From Eq. (2.3) we see that $e_{th}=1$ corresponds to 50% efficiency, independent of the value of $\sigma_{noise}$. Fig. 4 shows the efficiency for counting $2\,(3)\,e^{-}$ events as a function of the readout noise after imposing the conditions $e_{th}/\sigma_{noise}>5.4\,(4)$. Based on this analysis, to maintain an efficiency for counting $2\,(3)\,e^{-}$ events higher than 80% while complying with the Oscura background goal (requirement) we need $\sigma_{noise}<0.16\,(0.20)\,e^{-}$.

The high electric field generated in the CCD when the gate voltages change to move the charge from one pixel to the other can lead to the production of spurious charge (SC), also known as clock-induced charge [43]. This can happen either in the active area or in the serial register and it strongly depends on the clock rise time and the clock swings. The primary source of spurious charge is the clocking of the serial register, which tends to dominate over the slower vertical clocks due to the higher capacitance of the line across the CCD active region. Assuming that the probability of generating one electron on a single pixel transfer, $\kappa_{SC}$, is the same in both registers and considering that each pixel on the CCD is shifted $N_{ser}$ ($N_{par}$) times in the serial (parallel) register during readout, the 1$e^{-}$ rate coming from the spurious charge is

Oscura requires this component of the 1$e^{-}$ rate to be subdominant to the thermal dark current, $R_{SC,1e^{-}}<R_{DC,1e^{-}}$. Assuming $R_{DC,1e^{-}}=1\times 10^{-6}\,(1.6\times 10^{-4})\,e^{-}$/pix/day, $N_{exp}=12$ exposures/day, $N_{ser}=1058$ transfers/exposure, and $N_{par}=1278$ transfers/exposure, results in the condition $\kappa_{SC}<4\times 10^{-11}\,(6\times 10^{-9})\,e^{-}$/pix/transfer to reach the Oscura background goal (requirement).

Defects within the silicon lattice create intermediate energy levels within the Si bandgap that act like traps. These traps usually capture one electron from charge packets as they are transferred through the device and release the charge at a later characteristic time $\tau$ dependent on the temperature.

The number of 1$e^{-}$ events per sensor per exposure coming from traps is $N_{hits}\times N_{traps}$, where $N_{hits}$ is the number of hits, i.e., pixels with more than $2e^{-}$, in one exposure and $N_{traps}$ is the mean number of traps that a hit traverses during readout, which equals the total number of electrons trapped per hit assuming that each trap captures one electron. Only traps with a $\tau$ larger than the pixel readout time are considered because faster traps will release the trapped electron in the pixel containing the hit. The rate of $1e^{-}$ events produced from traps is calculated as

where $N_{pix}$ is the total number of pixels in each sensor.

We estimate $N_{hits}$ for Oscura assuming the baseline 1.35 Mpix sensors with 0.5 g of active mass and a background rate of 0.01 dru. In these conditions, we expect $N_{events}=5\times 10^{-4}$ events/exposure/sensor up to 100 keV in a one-day exposure, i.e., $N_{exp}=1$ exposure/day. Then, $N_{hits}=n_{pix}\times N_{events}$, where $n_{pix}$ is the expected number of pixels in one event with energy below 100 keV. As the number of pixels in one event is a broad distribution that increases towards less number of pixels, a conservative assumption is to take $n_{pix}=10$ pix/event. This results in

We require $R_{T,1e^{-}}<R_{DC,1e^{-}}=1\times 10^{-6}e^{-}$/pix/day to achieve both the Oscura background goal and requirement. This imposes the condition $N_{traps}<2.7\times 10^{2}$. Considering that each hit traverses a maximum of $N_{ser}+N_{par}=2336$ pix, the allowed density of traps is

This condition is satisfied if there is a trap every $\sim$8 pixels. Note that the allowed density of traps depends inversely on the background rate. Assuming a background rate one order of magnitude higher than the expected for Oscura, i.e. 0.1 dru, we get $\rho_{traps}<0.012$ traps/pix.

Charge transfer inefficiency (CTI) refers to the loss of charge when a charge packet is moved from one pixel to the next. It depends on several different parameters such as trap populations, trap densities, clocking time, clocking sequence, and temperature [43, 44, 45, 46]. CTI in the Oscura CCDs will result in the misidentification of $ne^{-}$ single pixel events into $(n-1)e^{-}$ events. The fraction of a $ne^{-}$ event in a single pixel that will be left in the subsequent pixel due to CTI is

where $k_{CTI}$ is the charge transfer inefficiency measured for a single pixel transfer within a row/column. Here, we are assuming a similar inefficiency for serial and parallel transfers. CTI is not an impediment to reach Oscura background goal/requirement as it does not change the total event rate. However, for a good performance, consistent with what is commonly achieved in CCDs, we establish as a target $\varepsilon_{CTI}<0.01$, which means $k_{CTI}<5\times 10^{-6}$.

As discussed above, the skipper-CCDs for Oscura will be operated in a LN2 pressure vessel. For a run on the surface and without any shield, we measure light generated in LN2 at a rate of $R_{LN2,1e^{-}}=0.013~{}e^{-}$/pix/day using a SENSEI skipper-CCD. The light is assumed to be produced by environmental radiation interacting in the LN2. For this measurement, the background around 10 keV was $\sim$$10^{4}$ dru, six orders of magnitude above the Oscura radiation background target of 0.01 dru. Assuming that light generation in LN2 scales with the background rate at higher energies, we estimate this light to produce $R_{LN2,1e^{-}}^{0.01\textrm{dru}}\sim$$10^{-8}~{}e^{-}$/pix/day in Oscura. This is much less than the expected thermal dark current in the Oscura sensors and it is not expected to contribute to the experimental background. We will check this simple assumption in next iterations of our experiment.

However, since the geometry and CCD packaging used to measure light generation in LN2 are not identical to the planned Oscura design, we are working to implement a light shield to ensure that ionization events from visible and near-IR light are a subdominant background. We aim to suppress more than $90$% of the light hitting the surface of the Oscura sensors.

Using an individually packaged Oscura prototype sensor, we measure the readout noise as a function of $N_{skp}$. The results, shown in Fig. 6, demonstrate that $N_{skp}=400\,(225)$ are enough to reach a noise of $0.15\,(0.19)\,e^{-}$, consistent with the constraints to achieve Oscura background goal (requirement) discussed in Section 2.2. However, increasing $N_{skp}$ also increases the readout time and the constraint on this parameter should also be met to comply with the Oscura background goal/requirement. In these measurements, the pixel readout time for $N_{skp}=400\,(225)$ was 15.3 (9) ms. This corresponds to a pixel readout rate of 65 (111) pix/s, allowing to read out the whole array in 5.8 (3.4) hours. Then, the readout time and noise constraints are both met only for the background requirement.

Tests were also performed in a system designed to host 16 MCMs, but with 10 MCMs installed. As mentioned in Section 1.1, each MCM has 16 Oscura prototype skipper-CCDs. Details and results from measurements with this system can be found in Ref. [48]. Fig. 7 shows the readout noise as a function of $N_{skp}$ for all the skipper-CCDs in the 10 MCMs. From these results, with $N_{skp}=480\,(300)$ the system reaches a noise of $0.16\,(0.20)\,e^{-}$ RMS, consistent with the constraints to achieve Oscura background goal (requirement) discussed in Section 2.2. In this system, the pixel readout time for $N_{skp}=480\,(300)$ is $t_{pix}=16.8\,(10.5)$ ms, plus an additional $t_{mux}=0.64$ ms for multiplexing the 16 MCMs. This corresponds to a pixel readout rate of 57 (89) pix/s, allowing to read out the whole array in 6.6 (4.2) hours. Again, the readout time and noise constraints are both met only for the Oscura background requirement. The system is yet to be optimized in its final configuration, which will enable it to achieve a higher pixel readout rate. The current system is still missing the MIDNA ASIC (Application Specific Integrated Circuit) [49], which will perform the analog pixel processing, and the flex cables used in this setup are longer than in the Oscura design. With shorter cables and the ASIC, the system will produce a faster signal due to reduced capacitance and the higher bandwidth of the MIDNA ASIC. This allows a reduction of the dead times in the readout sequence to get the maximum noise reduction per unit of readout time. The multiplexing time is also expected to be reduced using a faster ADC (Analog to Digital Converter) stage.

Note that we could achieve the readout rate necessary to reach the Oscura background goal by performing on-chip binning, i.e. combine the charge of adjacent pixels, during the readout, at the cost of reducing spatial resolution.

To quantify the Oscura sensors dark current (DC), we measured the exposure-dependent $1e^{-}$ rate as a function of temperature with an individually packaged Oscura prototype skipper-CCD in a dedicated setup with 2 inches of lead shield at surface. At a given temperature, we acquired images with different exposure times, from 0 to 30 min, with $N_{skp}=200$. To increase the readout rate, we performed a $5\times 1$ binning, i.e., the charge of 5 consecutive pixels in the same row was summed before readout. For the analysis, we selected the first rows of each image that were free of high-energy events. We perform linear fits to the plots of $1e^{-}$ rate as a function of exposure time, where the slopes correspond to the exposure-dependent $1e^{-}$ event rate. Fig. 8 (left) shows one of these plots corresponding to images taken at $T=150~{}\mathrm{K}$. We performed this measurement at different temperatures and the results, first presented in [47], are shown in Fig. 8 (right). The lowest value achieved was 0.03 $e^{-}$/pix/day, at 140 K.

This result is much larger than the rate needed to achieve the Oscura background requirement/goal. However, it is well known that, at surface, the main contribution to the $1e^{-}$ rate for $T<150~{}\mathrm{K}$ does not come from dark current but from low-energy radiation that is created when high-energy events interact with the detector components [15, 51, 52]. At surface, where the rate of events with energies above 0.5 keV is $\mathcal{O}\left(10^{4}-10^{5}\right)$, we expect a $\mathcal{O}\left(10^{-2}\right)$ $1e^{-}$ rate, consistent with the computation done in Ref. [51] for the SENSEI at MINOS setup, where a $\mathcal{O}\left(10^{-4}\right)$ $1e^{-}$ rate is expected from the $\sim$3 kdru high-energy background rate. Lower exposure-dependent $1e^{-}$ rates are expected when measurements can be made underground, in lower-background environments.

From the measurements described in Section 3.2, we extract an upper limit for the generated spurious charge from the y-intercept of the linear fits. The average value is $8.4\times 10^{-4}e^{-}$/pix. Considering that in these measurements each read pixel underwent $(N_{par}+N_{ser})/2=1168$ transfers/exposure, this corresponds to $\kappa_{SC}=7.2\times 10^{-7}e^{-}$/pix/transfer.

Following an analogous procedure as the one described in [53], we measured the generation of charge in the output stage. Using an individually packaged Oscura prototype sensor, we read out 20 pixels with 5 million skipper samples, clocking only the output stage. We obtained an average rate of $\sim$$1\times 10^{-7}e^{-}$/sample.

With the SENSEI skipper-CCD used to measure light generation in LN2 we also computed the generated spurious charge. The data shows that the total number of $1e^{-}$ events produced by the spurious charge per pixel is $\sim$$10^{-4}$. As in this CCD $(N_{par}+N_{ser})\simeq 7000$, this gives $\kappa_{SC}\simeq 1.4\times 10^{-8}e^{-}$/pix/transfer.

In all cases we measure a $\kappa_{SC}$ higher than what is needed to meet Oscura background requirement/goal. Members of the Oscura collaboration are working to better understand spurious charge generation in skipper-CCDs. To reduce it, we are considering several approaches, including the use of filtering techniques to decrease the slew rates of horizontal clock signals, as well as implementing shaped clock signals [54].

We use the charge pumping technique [55, 43, 56, 57] to localize and characterize traps in individually packaged skipper-CCDs. This popular method consists of filling the traps and allowing them to emit the trapped charge in their neighbor pixel multiple times. This is done by repeatedly moving, back and forth between the phases³³3A pixel phase refers to a gate (electrode) laying on the CCD front surface in which clocking voltages are applied [43]. in one pixel, a uniform illuminated field creating "dipole" signals relative to the flat background.

Using a violet LED externally controlled by an Arduino Nano, we uniformly illuminated the three-phase skipper-CCDs and performed a charge pumping sequence that probes traps below pixel phases 1 and 3. We collected images varying the time that charge stayed below the pixel phases ($dt_{ph}$). We identified and tracked the position of each dipole in the set of images, computed its intensity as a function of $dt_{ph}$ and fitted it. From the fits, we extracted the characteristic release time $\tau$ for each of the found traps. We did this at different temperatures.

Fig. 9 shows images revealing traps with characteristic time $\tau>3.34$ ms, corresponding to $dt_{ph}=50000$ clocks, for two Oscura prototype sensors with different fabrication process. The four images in the top row, corresponding to each of the four amplifiers in prototype-A, show a much more significant density of dipoles compared to the images in the bottom row, corresponding to each of the amplifiers in prototype-B.

The histograms in Fig. 10 show the number of traps per pixel as a function of $\tau$ for two different Oscura prototype skipper-CCDs and a SENSEI skipper-CCD, at two different temperatures. These histograms correspond to traps below pixel phases 1 and 3 and no detection efficiency was taken into account. Considering a uniform density of traps below the three phases in each pixel and assuming a conservative 10% detection efficiency with a flat profile, the y-axis in Fig. 10 should be multiplied by a factor of 15 to obtain a more realistic trap density.

Traps with a release time greater than the pixel readout time will generate $1e^{-}$ events in the images. Considering the pixel readout rate needed to achieve Oscura background goal, traps with a release time $\tau>5.3$ ms should satisfy the trap density constraint. In the case of the Oscura prototype-A, the realistic number of traps with $\tau>5.3$ ms below 170 K is $\sim$$1.5\times 10^{-2}$. For the Oscura prototype-B and the SENSEI skipper-CCD, this number is 2 orders of magnitude lower ($\sim$$3\times 10^{-4}$). Despite this difference, both Oscura prototype skipper-CCDs meet the constraint needed to reach the background goal/requirement.

However, as discussed in Section 2.4, if Oscura overall background is one order of magnitude higher (0.1 dru), the Oscura prototype-A would barely meet the constraint. For this reason in a cooperative effort with the foundry that fabricated this sensor, we are trying to implement a different gettering method during the fabrication process to reduce possible impurities in the silicon.

We exposed an individually packaged Oscura prototype skipper-CCD to a Fe⁵⁵ X-ray source. We took images with 4 skipper samples applying the usual clocking sequence and voltages. We computed the parallel and serial registers CTI at different operational temperatures by linearly fitting the pixel population associated with X-ray depositions from X-ray transfer plots [43], see Fig. 11. This figure shows the scatter plots of the pixel values versus its column (left) and row (right) numbers from a set of images acquired at 170 K. In all cases, we computed a $k_{CTI}<5\times 10^{-5}$, which is slightly higher than the target. Note that these measurements were done using a Oscura prototype-A sensor with a high-density of traps and, as traps contribute to CTI, this number should be reduced by addressing this issue and optimizing the clocking sequence.

We deposited a 50 nm aluminum layer on top of the active area of Oscura prototype skipper-CCDs using a maskless lithography tool (Heidelberg MLA 150) and an electron beam evaporator (Temescal FC200). Within the first tests we produced a prototype with a shaped aluminum layer on top of each quadrant, as shown in Fig. 12 (left), where the wire bonds between the pads and the flex cable that connects the sensor to the readout electronics are also shown. Fig. 12 (right) shows an image taken with the upper half of the CCD after 30 min of exposure in a testing setup that was not completely shielded from environmental light. Electron, X-ray, and muon tracks are uniformly distributed in the active area, while the background light under the aluminum layer is $\sim$95% suppressed compared to that in an uncovered area. Although the process implemented to produce this device is not optimal since the beam evaporator can damage the CCD, the result sufficed as proof of concept for the next fabrication step. A thicker aluminum layer can be safely incorporated as a part of the sensor production and will guarantee meeting the light suppression target.