Performance of a Large Area Photon Detector For Rare Event Search Applications

We present the design and characterization of a large-area Cryogenic PhotoDetector (CPD) designed for active particle identification in rare event searches, such as neutrinoless double beta decay and dark matter experiments. The detector consists of a $45.6$ $\mathrm{cm}^2$ surface area by 1-mm-thick $10.6$ $\mathrm{g}$ Si wafer. It is instrumented with a distributed network of Quasiparticle-trap-assisted Electrothermal feedback Transition-edge sensors (QETs) with $T_c=41.5$ $\mathrm{mK}$ to measure athermal phonons released from interactions with photons. The detector is characterized and calibrated in the center of the detector with a collimated $^{55}$Fe X-ray source. The noise equivalent power is measured to be $1\times 10^{-17}$ $\mathrm{W}/\sqrt{\mathrm{Hz}}$ in a bandwidth of $2.7$ $\mathrm{kHz}$. The baseline energy resolution is measured to be $\sigma_E = 3.86 \pm 0.04$ $(\mathrm{stat.})^{+0.23}_{-0.00}$ $(\mathrm{syst.})$ $\mathrm{eV}$ (RMS). The detector also has an expected timing resolution of $\sigma_t = 2.3$ $\mu\mathrm{s}$ for $5$ $\sigma_E$ events.

In rare event searches, experimental sensitivity is often limited by background signals [1][2][3][4][5][6][7][8][9] . Developing precision detectors to veto background and noise signals has been a high priority in these fields. Much interest in low temperature cryogenic detector technology has been shown by groups carrying out searches for neutrinoless double beta decay 10 (0νββ), such as the CUORE 11 , CUPID 12 , and AMoRE 13 experiments. For these searches, the dominant source of background events consists of α decays from the surrounding environment 1,14 . It has been shown that Cherenkov emission or scintillation light can be used to positively identify the signal βs, allowing for background discrimination 15 . In order for these experiments to achieve a high level of rejection for these α backgrounds, photon detectors with large surface areas and sub-20 eV baseline energy resolutions are required 12,14 . To reject the pileup background from multiple ordinary (two neutrino) double beta decay (2νββ) events, experiments need timing resolutions down to 10 µs (for the 100 Mo isotope) 12 .
There has also been theoretical and experimental motivation to search for dark matter (DM) in the mass range of keV/c 2 to GeV/c 2 16-19 . However, current experiments have been limited by unknown background signals in the energy range of O(1-100) eV [3][4][5][6][7][8][9]20 . If the source of such backgrounds are high energy photons that deposit only an extremely small fraction of their energy in the target 21 , then a nearly 4π active shield composed of high-Z scintillating crystals surrounding the detector could be highly efficient at suppressing these backgrounds. Additionally, a sensitive large area cryogenic detector could be useful for discriminating small energy depositions due to radiogenic surface backgrounds. Other potential DM applications for this detector technology include searches for inelastic electronic recoils off scintillating crystals and searches for interactions with superfluid He 22,23 .
We present the characterization of a large area Cryogenic PhotoDetector (CPD) with a measured baseline energy resolution of 3.86 ± 0.04 (stat.) +0. 23 −0.00 (syst.) eV (RMS) and a timing resolution of 2.3 µs for 20 eV events that meets the technical requirements for the use cases discussed above.
The (100)-oriented substrate of the CPD is a 10.6 g Si wafer of thickness 1 mm and a surface area of 45.6 cm 2 . A parallel network of 1031 Quasiparticle-trap-assisted Electrothermal feedback Transition-edge sensors (QETs) 24,25 with T c = 41.5 mK was deposited on one side of the wafer. The QETs are uniformly distributed over the wafer's surface and connected to a single readout channel. The uniform and distributed nature of the channel allows for the fast collection of athermal phonons with minimal positional dependence, reducing efficiency penalties from ef- fects such as athermal phonon down-conversion 26,27 . The opposite side of the Si wafer is unpolished and noninstrumented. The detector and QET mask design can be seen in Fig. 1. In Table I, the QET design specifications for the CPD are listed.
The detector was studied at the SLAC National Accelerator Laboratory in a cryogen-free dilution refrigerator at a bath temperature (T B ) of 8 mK. The detector was placed in a copper housing and was held mechanically with the use of six cirlex clamps. The cirlex clamps also provided the thermal link between the detector and the copper housing. The QET arrays were voltage biased and the current through the TES was measured with a DC superconducting quantum interference device (SQUID) array with a measured noise floor of ∼ 4 pA/ √ Hz. A collimated 55 Fe X-ray source was placed inside the cryostat and was incident upon the noninstrumented side of the CPD in the center of the detector. A layer of Al foil was placed inside the collimator to provide a calibration line from fluorescence at 1.5 keV 28,29 . The collimator was tuned such that there was ∼ 5 Hz of the K α and K β decays incident on the detector. The detector was held at a TABLE II. Fitted calculated parameters of the TES from IV curves. The systematic errors on GT A and Tc represent the upper bound on these values, using the hypothesis that the observed excess noise in the sensor bandwidth is entirely due to parasitic bias power.
bath temperature T B T c for approximately two weeks to allow any parasitic heat added by the cirlex clamps to dissipate. During this time, we attempted to neutralize potential charged impurities within the Si wafer as much as possible with ionization produced by a 9.13 µCi 137 Cs source placed outside of the cryostat.
To characterize the QETs, IV sweeps were taken at various bath temperatures by measuring TES quiescent current as a function of bias current 30 , with superimposed small square pulses providing complex admittance 24 at each point in the IV curve [31][32][33] . Since all the QETs are connected in parallel in a single channel, the channel was treated as if it were a single QET, describing the average characteristics of the total array. The IV data allowed for the estimation of the parasitic resistance in the TES line (R p ), the normal state resistance (R N ), and the nominal bias power (P 0 ). The effective thermal conductance between the QETs to the Si wafer (G T A ) and T c were measured by fitting a power law to the measured bias power as a function of bath temperature 31 . This measurement is a lower bound of these values, as it assumes no parasitic bias power in the system. We summarize these characteristics of the detector in Table II. The complex admittance data allows us to estimate the dynamic properties of the sensors. Throughout the superconducting transition, primary and secondary thermal fall times were observed, e.g. 58 µs and 370 µs, respectively, at R 0 ≈ 35% R N . The origin of this additional time constant is under investigation. Its appearance suggests that we have a more complex thermal or electrical system, e.g. phase separation 32,34 or an extra heat capacity connected to the TES heat capacity 35 . A characteristic plot of complex impedance of the TES circuit can be seen in Fig. 2.
Knowledge of the TES parameters allowed for the calculation of the power-to-current responsivity, which was used to convert the measured current-referred power spectral density (PSD) to the noise equivalent power (NEP). These parameters were used to predict the expected noise spectrum using the single-heat-capacity thermal model 24    is also elevated above our model at frequencies in the effective sensor bandwidth interval (approximately the inverse of the thermal time constant τ − 24 ) by a factor of ∼ 2, as compared to the prediction. This "in-band" excess noise is consistent with two different hypotheses: a white power noise spectrum incident on the detector of 8 × 10 −18 W/ √ Hz (e.g. a light leak) or a parasitic DC power in the bias circuit of approximately 6 pW. If we assume the latter is the source, this allows us to calculate the upper bound on our estimates of G T A and T c , as reported in Table II. There remains bias-dependent excess noise above the sensor bandwidth. We parameterize the excess TES Johnson-like noise with the commonly used M factor 24,36 . Using values of M up to 1.8, depending on bias point, can account for the discrepancy between observation and prediction at these frequencies.
The lowest integrated NEP was achieved at an op-timum bias point of R 0 = 31 mΩ ≈ 35%R N . In addition to the characterization data, approximately 500, 000 threshold triggered events and 80, 000 randomly triggered events were recorded at this bias. For the measured phonon-pulse shape, there are multiple characteristic time constants. The dominant pulse fall time is consistent with the expectation from the complex impedance as we approach zero-energy, where we confirmed the expected thermal time constant τ − = 58 µs via nonlinear least squares. The secondary time constant from the complex impedance of 370 µs was also seen in these low-energy pulses, with an amplitude ratio of ∼ 2% to the dominant decay exponential. For higher energies, we observed a local saturation effect that manifests as the dominant fall time lengthening with increased energy. We associate this effect with high-energy, singleparticle events pushing nearby QETs into the normal resistance regime, slowing down the response of the total single-channel device. This effect is specific to the singleparticle nature of the measured events. For scintillation events, the isotropic nature of the photons would spread out the event energy across the entire detector channel, avoiding these local saturation effects. In Fig. 4, we show averaged pulses for various event amplitudes, showing the dependence of the pulse fall time on energy. The pulse rise time was measured as τ ph = 20 µs, which is the expected characteristic time scale for athermal phonons being absorbed by the Al collection fins of the QETs for this design. We also observed long-lived behavior in the pulses, which can be estimated as a low-amplitude ∼ 3 ms exponential tail whose magnitude scales linearly with the event energy. As this tail is not seen in the complex impedance data, it might be due to direct absorption of phonons with energy smaller than the Al superconducting band gap into the TES 25 .
To reconstruct event energies, two energy estimators were used in this analysis: the optimum filter (OF) amplitude 37,38 and the energy removed by electrothermal feedback (E ETF ) 24 . For the OF, we used an offline algorithm to reconstruct energies. A single noise spectrum was used, which was computed from the randomly triggered events. The phonon-pulse template used was an analytic template that matches the measured lowenergy pulse shape, neglecting the 3 ms low-amplitude tail. Because we could not directly measure the lowenergy phonon-pulse shape with high statistics, we used a template without the long-lived behavior.
The integral estimator E ETF was calculated for each triggered event by measuring the decrease in Joule heating via (1) where T is the time at which the integral is truncated, ∆I(t) is the baseline-subtracted pulse in current, I 0 is the quiescent current through the TES, R is the load resistance, and V b is the voltage bias of the TES circuit 24 . In comparison to the OF amplitude, this integral esti- mator was less sensitive to saturation effects, but had a worse baseline energy resolution. When characterizing this device, we used the integral truncation of T ≈ 7τ − for E ETF . This was done to preserve good baseline energy sensitivity in this integral estimator when calibrating the OF amplitude energy estimator at low energies. For pulse-shape saturation at high energies, we use the following empirical model: This functional form has the expected behavior: it intercepts zero, approaches an asymptotic value at high energies, and becomes linear for small values of E true . In Fig. 5, the fitted saturation model, as well as the calibrated and uncalibrated E ETF spectra, are shown, as compared to the energies of various spectral peaks in both energy scales. The absolute phonon collection efficiency (ε ph ) of the detector was estimated by measuring E ETF at the lowest energy calibration line (Al fluorescence) and dividing by the known energy of that line. Because of the longlived behavior in the phonon-pulse shapes, the measured collection efficiency of this detector depends on the integration truncation time T . If it is chosen to only include energy collected by the first sensor fall time τ − (e.g. T ≈ 7τ − ), then we find that ε ph = 13 ± 1%. Alternatively, if we integrate to effectively infinity, this includes the low-amplitude long-lived behavior of the phonon pulses. In this case, the collection efficiency in- creases to ε ∞ ph = 17 ± 1%, which implies that about 30% of the collected energy for a given event is associated with the low-amplitude tail of the phonon-pulse shape.
To calibrate the OF amplitude to units of energy, we fit the relationship between the calibrated E ETF and the OF amplitude to a linear slope at low energies (below approximately 300 eV). This method does not provide a calibration of the OF amplitude at high energies, but allows for the calculation of the baseline energy resolution.
For the calibration method used, the main source of systematic error is the saturation model in Eq. (2). Since it is empirical, its use introduces uncertainty in its applicability. We can estimate the upper bound of the effect of this systematic on the baseline energy resolution as the value that would be reached if we instead calibrated E ETF linearly using the Al fluorescence line. In this case, this worsens the baseline energy resolution, as we are not taking into account the expected response (see Fig. 5).
The baseline energy resolution was calculated as the RMS of 46,000 randomly triggered events, after removing data contaminated by pileup events, electronic glitches, or thermal tails. This gave a resolution of σ E = 3.86 ± 0.04 (stat.) +0. 23 −0.00 (syst.) eV (RMS) for the OF energy estimator, where these data are consistent with a normal distribution. This is in agreement with our estimation from the observed NEP and the power-referred phonon-pulse shape (a single-exponential with fall time τ ph and collection efficiency ph ), which gave an expected baseline energy resolution of σ th E = 3.9 ± 0.4 eV (RMS). Using the OF formalism, we can also calculate the expected timing resolution 38 of the CPD, which provides an estimate of the minimum resolving time for two pileup events. For a 5σ event, the corresponding timing resolution of this detector is 2.3 µs. For many 0νββ experiments, the timing resolution requirement to make pileup of multiple 2νββ events a negligible background is on the order of 1 ms [40][41][42][43] . For the CUPID and CUPID-1T experiments, this requirement is about 300 µs and 10 µs, respectively 12 . Thus, we expect the CPD to fulfill these requirements.
When comparing the baseline energy resolution of the CPD to the requirements of the CUPID experiment, the value surpasses the requirement of less than 20 eV (RMS) by a factor of five. While the CPD is a TES-based detector, it has been shown that Microwave Kinetic Inductance Detectors (MKIDs) and Neutron-Transmutation-Doped (NTD) Ge detectors are also promising avenues for achieving the sub-20 eV baseline goal. In Table III, we report this result alongside those of other detectors for this application. In comparison to the devices that have met or exceeded the requirement, the CPD does not require Neganov-Trofimov-Luke (NTL) amplification 44,45 (which often results in excess dark counts) and has the best baseline energy sensitivity for its size.
The measured baseline energy resolution of 3.86 ± 0.04 (stat.) +0. 23 −0.00 (syst.) eV and the expected timing resolution of 2.3 µs (at 5σ E ), combined with its large surface area, makes this detector an excellent candidate for background rejection in both 0νββ and DM experiments.
Because of the excellent energy sensitivity, this device can be used as a dark matter detector itself, as we have done in collaboration with SuperCDMS to set limits on spin-independent dark matter-nucleon interactions for sub-GeV/c 2 dark matter particle masses 55 . The performance of the CPD can be further optimized through adjustment of characteristics such as the Al-W overlap and overall Al coverage. From these considerations, we anticipate up to a factor of two improvement in baseline energy resolution for a future iteration of the CPD, which is currently being designed.
This material is based upon work supported by the The data that support the findings of this study are available upon reasonable request to the corresponding authors.