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

This paper identifies spontaneous athermal phonon bursts originating from the bulk silicon substrate as the dominant source of low-energy background events and excess noise in superconducting sensors, demonstrating that these bursts scale linearly with substrate thickness and relax over time, thereby establishing a critical link to quasiparticle poisoning in superconducting qubits.

The Gist

Imagine you are trying to listen to a whisper in a room that is supposed to be perfectly silent. You have built the most sensitive microphone in the world—a "super-sensor" made of silicon and cooled to a temperature colder than deep space. Your goal is to hear the faintest possible signals, like a ghostly dark matter particle or a tiny neutrino bumping into an atom.

But there's a problem. Even when you think the room is empty, your microphone is picking up a constant, static-like "hiss" and sudden, tiny pops. This is the "Low Energy Excess" (LEE). It's like trying to hear a pin drop while someone is constantly dropping tiny pebbles on the floor nearby.

This paper is the story of a team of scientists (the TESSERACT Collaboration) who acted like detectives to figure out where these pebbles are coming from.

The Mystery: The "Ghost" Noise

The scientists had two nearly identical silicon detectors. They were like twins, except one was thin (1 mm thick, like a thick coin) and the other was thick (4 mm thick, like a small brick). Both were made of the same high-quality silicon and had the same super-sensitive sensors glued to them.

They expected the noise to come from the sensors themselves (the "microphone" part). But when they started listening, they found something strange:

• The thick detector was making four times more noise than the thin one.
• The noise wasn't just random; it was a burst of energy (a "phonon burst") that looked like a tiny earthquake inside the silicon.

The Investigation: Volume vs. Surface

To solve the mystery, the scientists had to guess where the noise was hiding. They considered three suspects:

1. The Surface (The Walls): Maybe the noise was coming from the rough edges where the silicon was cut (the sidewalls).
2. The Sensors (The Microphone): Maybe the metal films on top were vibrating or relaxing.
3. The Bulk (The Room): Maybe the noise was coming from deep inside the silicon block itself.

The Clue: Because the thick detector (4x the volume) made 4x the noise, the scientists realized the noise wasn't coming from the surface or the sensors. If it were, the thick and thin detectors would have made roughly the same amount of noise.

The Verdict: The noise is coming from the bulk of the silicon itself. It's as if the silicon brick is "relaxing" or "settling" after being cooled down, releasing tiny bursts of energy from deep within its atomic structure.

The "Settling In" Phenomenon

Here is the most fascinating part: The noise gets quieter over time.

When the scientists first cooled the detectors down, the noise was loud. But as they waited (over 12 days), the "pebbles" stopped dropping as often.

• Analogy: Imagine a jar of marbles that you just shook up. At first, they are rattling around wildly. But if you leave the jar alone for a few days, the marbles eventually settle into a quiet, stable pile. The silicon is doing the same thing. The internal defects (tiny imperfections in the crystal) are "relaxing" from a high-energy state to a low-energy state, and once they settle, the noise stops.

Why Should You Care?

You might think, "I don't have a super-sensitive dark matter detector in my basement." But this discovery is huge for two other reasons:

1. Better Dark Matter Hunting: To find dark matter, we need to know exactly what "background noise" looks like so we don't mistake a silicon burp for a dark matter particle. Now that we know the noise comes from the silicon's volume and fades with time, we can design better experiments and wait for the noise to settle before we start listening.
2. The "Quasiparticle Poisoning" of Quantum Computers: This is the big one for the future. Quantum computers (like the ones Google and IBM are building) use tiny circuits made of superconductors sitting on silicon chips.
   • The Problem: These quantum bits (qubits) are incredibly fragile. If a tiny burst of energy (a phonon) hits them, it can break the superconducting state and ruin the calculation. This is called "quasiparticle poisoning."
   • The Connection: This paper suggests that the silicon chip underneath the quantum computer is spontaneously generating these energy bursts. Even if your quantum computer is in a perfect, vibration-free, shielded room, the silicon itself might be "poisoning" the computer from the inside out.

The Bottom Line

The scientists found that the "ghost noise" in their detectors isn't coming from the sensors or the edges, but from the bulk silicon itself as it cools down and relaxes.

• Thicker silicon = More noise.
• Waiting longer = Less noise.
• The energy of these bursts is tiny (about the size of a single electron's energy in aluminum), but enough to mess up sensitive experiments.

This discovery is like realizing that the floorboards in your house are creaking not because of the wind or the people walking, but because the wood itself is slowly drying out and settling. Once you know that, you can stop blaming the wind and start waiting for the wood to settle down so you can finally hear that whisper.

Technical Summary

1. Problem Statement

Solid-state phonon detectors are critical for searching for light dark matter and detecting Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS). These applications require detectors with eV-scale energy resolution and extremely low background rates. However, current low-threshold detectors suffer from a pervasive "Low Energy Excess" (LEE)—a background of events below a few hundred eV that is orders of magnitude higher than expected from radioactivity or cosmic rays.

This excess manifests in two ways:

1. Above-threshold events: Real background events that obscure rare signal searches.
2. Below-threshold shot noise: Sub-threshold phonon bursts that generate excess shot noise, degrading energy resolution and potentially causing "quasiparticle poisoning" in superconducting qubits.

The origin of these events has been debated, with hypotheses ranging from surface defects to sensor film relaxation. This paper aims to identify the dominant source by isolating the scaling behavior of these backgrounds with respect to the detector substrate.

2. Methodology

The TESSERACT collaboration conducted a controlled experiment comparing two nearly identical silicon phonon detectors to isolate the effect of substrate thickness.

• Detector Design: Two 1 cm$^2$ silicon detectors were fabricated using identical Transition Edge Sensor (TES) and Quasiparticle-trap-enhanced Electrothermal-feedback Transition Edge Sensor (QET) architectures.
  • Detector A: 1 mm thick silicon substrate (Mass: 0.233 g).
  • Detector B: 4 mm thick silicon substrate (Mass: 0.932 g).
  • Both used Tungsten TESs ($T_c \approx 50$ mK) coupled to Aluminum phonon collection fins.
• Experimental Setup: Both detectors were suspended by wire bonds inside an IR and EMI-shielded housing attached to a dilution refrigerator mixing chamber. They were fabricated in the same facility within one week to minimize systematic differences.
• Data Collection:
  • Calibration: Used 450 nm (2.755 eV) photon pulses to map energy response and distinguish between "single" (sensor-localized) and "shared" (substrate-originated) events.
  • Noise Analysis: Recorded continuous data for 12 days post-cooldown. Used optimal filtering to separate correlated noise (shared between channels) from uncorrelated noise.
  • Background Analysis: Triggered on events with pulse shapes consistent with substrate-absorbed photons to measure the rate of "shared" LEE events.
• Scaling Comparison: The authors compared their results with previous data from other silicon detectors (SPICE, CPD, CRESST) with different geometries (volume-to-sidewall ratios) and mounting strategies.

3. Key Contributions & Findings

A. Substrate Thickness Scaling

The most significant finding is that both the correlated phonon shot noise (below threshold) and the shared LEE background rate (above threshold) scale linearly with the substrate thickness (and thus volume).

• The 4 mm detector exhibited approximately 4 times the correlated noise and shared background rate of the 1 mm detector.
• This linear scaling strongly suggests the source is distributed throughout the bulk volume of the silicon substrate, rather than being confined to the surface, sidewalls, or sensor films.

B. Temporal Relaxation

Both the correlated noise and the shared LEE rates were observed to relax (decrease) over time following the cooldown of the detector.

• The noise amplitude and the bias power required to maintain the TES transition both decreased over the 12-day run.
• The decay follows a power law ($t^{-\kappa}$) with $\kappa \approx 0.635$.
• This time dependence suggests a mechanism involving the thermal relaxation of defects or stress states that were populated at room temperature and are slowly relaxing at mK temperatures.

C. Energy Scale of Sub-threshold Events

By correlating the excess shot noise power with the parasitic bias power, the authors estimated the characteristic energy scale ($\epsilon$) of the sub-threshold phonon bursts.

• Result: $\epsilon = 0.68 \pm 0.38$ meV.
• Significance: This energy scale is comparable to the aluminum superconducting bandgap ($2\Delta_{Al} \approx 360$ $\mu$eV). This implies that these bursts are energetic enough to break Cooper pairs in the sensor fins, generating quasiparticles.

D. Rejection of Alternative Hypotheses

• Sensor Films: The linear scaling with volume rules out the aluminum or tungsten sensor films as the dominant source of shared events (which would be surface-area dependent).
• Sidewalls: While sidewall damage is a candidate, the comparison with large-area cylindrical detectors (CPD) suggests that volume scaling fits the data better than sidewall area scaling.
• Mounting Stress: The consistency of volume scaling across different mounting methods (wire bonds vs. clamps) suggests the source is intrinsic to the bulk silicon, not just mechanical stress from holding.

E. Quasiparticle Poisoning in Qubits

The authors modeled the impact of these silicon substrate phonon bursts on superconducting qubits.

• They estimated that bulk silicon phonon bursts could generate a residual quasiparticle density ($x_{qp}$) of $\approx 10^{-8} - 10^{-7}$ in modern qubits.
• This aligns with observed residual quasiparticle densities in non-gap-engineered qubits, suggesting that bulk silicon defects are a significant, previously underappreciated source of decoherence even in well-shielded, vibration-free environments.

4. Results Summary

• Energy Resolution: Achieved a world-leading baseline phonon energy resolution of 258.5 $\pm$ 0.4 meV in the 1 mm detector.
• Noise Origin: Confirmed that the dominant source of low-energy excess noise and backgrounds in these detectors is the bulk silicon substrate.
• Mechanism: Likely caused by the relaxation of crystal defects (e.g., neutron-induced damage or dislocation-mediated stress relaxation) where meV-scale energy gaps are thermally populated at 300 K and relax at mK temperatures.
• Time Dependence: The noise and background rates decrease significantly over time (power law decay), implying that "aging" the detector after cooldown can improve performance.

5. Significance

This work provides a definitive identification of the bulk silicon substrate as the primary source of low-energy backgrounds in phonon-mediated detectors. This has profound implications for:

1. Dark Matter Searches: Future detectors must account for bulk silicon defects. Strategies to mitigate this may include using higher-purity silicon, specific thermal histories, or waiting for the "relaxation" period after cooldown.
2. Superconducting Quantum Computing: The study links bulk silicon phonon bursts directly to quasiparticle poisoning in qubits. This suggests that improving the quality of the silicon substrate or engineering the interface between the substrate and superconductors is crucial for extending qubit coherence times, even in the absence of external radiation.
3. Detector Design: It establishes that simply reducing surface area or changing mounting techniques is insufficient; the volume of the substrate is the critical parameter governing background rates.