Spontaneous generation of athermal phonon bursts within bulk silicon causing excess noise, low energy background events and quasiparticle poisoning in superconducting sensors

TL;DR

This work probes the origin of the low energy excess (LEE) and correlated phonon shot noise in silicon-based solid-state phonon detectors used for dark matter and CEνNS searches. By comparing two 1 cm^2 silicon detectors with 1 mm and 4 mm substrates, the authors quantify how sub-threshold noise and above-threshold backgrounds scale with substrate volume, finding a bulk silicon origin for these bursts. They report a world-leading energy resolution of $258.5\pm0.4$ meV and extract a subthreshold energy scale of $\varepsilon = 0.68\pm0.38$ meV, consistent with phonon bursts in the substrate. The results imply potential quasiparticle poisoning in superconducting devices on silicon and provide a simple quasiparticle-dynamics framework to connect substrate phonon bursts to device performance, with broad implications for low-background detectors and quantum sensors.

Abstract

Solid state phonon detectors used in the search for dark matter and coherent neutrino nucleus interactions (CE$ν$NS) require excellent energy resolution (eV-scale or below) and low backgrounds. An unknown source of phonon bursts, the low energy excess (LEE), dominates other above-threshold backgrounds and generates excess shot noise from sub-threshold bursts. In this paper, we measure these phonon bursts for 12 days after cooldown in two nearly identical 1 cm$^2$ silicon detectors that differ only in the thickness of their substrate (1 mm vs. 4 mm thick). We find that both the channel-correlated shot noise and near-threshold shared LEE relax with time since cooldown. Additionally, both the correlated shot noise and LEE rates scale linearly with substrate thickness. When combined with previous measurements of other silicon phonon detectors with different substrate geometries and mechanical support strategies, these measurements strongly suggest that the dominant source of both above and below threshold LEE is the bulk substrate. By monitoring the relation between bias power and excess phonon shot noise, we estimate that the energy scale for sub-threshold noise events is $0.68 \pm 0.38$ meV. In our final dataset, we report a world-leading energy resolution of 258.5$\pm$0.4 meV in the 1 mm thick detector. Simple calculations suggest that these silicon substrate phonon bursts are likely a significant source of quasiparticle poisoning in superconducting qubits operated in well shielded and vibration free environments.

Figures (16)

• Figure 1: (Top left) Photograph of our 1 mm (left) and 4 mm thick (right) 1 cm$^2$ silicon detectors. (Top right) Detail on mask design for our phonon sensors (QETs). For scale, the QET fins have a radius of approximately 140 $\mu$m. (Bottom) Sketch of backgrounds and shot noise sources we observe in our devices. Shared LEE backgrounds and correlated phonon shot noise appear at approximately 4x the rate in the 4 mm detector compared to the 1 mm detector.
• Figure 2: 1 mm device calibration. (Left) Two dimensional histogram of calibration events. Most calibration photons hit the substrate, causing even responses in both channels (main diagonal events). Due to the energy resolution of our detector, individual photons appear as quantized quasi-Gaussian groups. Occasionally, photons hit a phonon sensor (QET), causing a large response in that channel (offset events). Around 1.1 eV of each 2.755 eV photon is absorbed in our sensors due to our phonon collection efficiency. (Top Right) Photon calibration spectra taken on days 2, 5, and 12. Note the improvement on baseline resolution over time. (Bottom Right) Measured phonon energy resolutions in the right, left, and combined channels over time.
• Figure 3: (Left) Noise in the left channels of the 1 mm (top, green) and 4 mm (bottom, blue) detectors. Our noise is well in excess of our modeled TES noise (gray, dotted), and is composed of correlated phonon noise and uncorrelated noise as in Ref. TwoChannelPaper. The peaks around 150 Hz are due to vibration coupled noise. Grey dashed lines show the primary (electrothermal) pole of the TES. (Top Right) Correlated noise (i.e. off diagonal CSD element $S_{LR}$) in the 4 mm and 1 mm detectors. The correlated noise in the 4 mm detector is 4 times as large as the 1 mm detector. The amplitude of the 1 mm correlated noise is fit in the orange highlighted region (to avoid vibration coupled peaks), while the 4 mm noise is fit in the orange and yellow regions. Dashed green and blue lines show the primary phonon poles of the 1 mm and 4 mm detectors respectively. (Bottom Right) Uncorrelated noise (i.e. $S_{LL}$, with the modeled correlated noise subtracted) in the left channels of the 1 mm and 4 mm detectors, consistent with the modeled TES Johnson noise at high frequencies and an excess noise term that is approximately flat and consistent between the two channels at low frequencies (see section \ref{['appendix:uncorrelated_noise']} for further discussion). Data corresponds to the final (day 12) dataset.
• Figure 4: Correlated noise level (Top Left) and Left + Right channel bias powers (Bottom Left) in the 1 mm (green) and 4 mm (blue) detectors as a function of time. (Right) Correlated noise level vs. Left + Right bias powers. Dashed lines show fit models, representing shot noise that scales in rate with detector volume with a shot noise quantum of $\varepsilon = 0.68 \pm 0.38$ meV, comparable to the aluminum superconducting bandgap.
• Figure 5: (Top) The mass normalized shared background rates in the 1 mm and 4 mm detectors, with backgrounds measured in the SPICE 1%TwoChannelPaperTwoChannelLimits, CPDv1finkPerformanceLargeArea2021CPDLimits, CPDv2 (previously unpublished), and CRESST 0.35g Si angloherLatestObservationsLow2022 detectors. Broadly, all six detectors seem to observe the same backgrounds normalizing for mass. Note that as the CPD and CRESST detectors are one channel detectors which cannot reject singlesTwoChannelPaper, the increased background rates near threshold could be due to singles, as well as noise triggers or additional LEE backgrounds. For clarity, the 1 mm, 4 mm, and SPICE 1% detectors have their spectra cut off at 30 eV to remove saturated events from cosmic rays and radioactive backgrounds which begin to appear at these energies. (Top insert) Detail of the 1 mm, 4 mm, and SPICE 1% detector backgrounds. The orange and green bands show the energy ranges in which time dependence was measured (see bottom right). (Left Bottom) Background event energy partitioning between left and right channels, showing single and shared events. Note the energy reconstruction assumes a shared pulse shape in each channel. (Right bottom) Rate of shared events over time in the 1 mm detector in the shaded 2.5-5 eV and 5-10 eV bins in the center top figure. Dashed line shows the (weighted) average rate in the 5-10 eV range, and a power law fit in the 2.5-5 eV bin.