SiPM non-linearity studies in beam tests with scintillating crystals

This paper presents beam test results at CERN demonstrating that high-pixel-density SiPMs coupled to BGO and BSO crystals exhibit significant non-linear responses, with deviations reaching approximately 20% at high photoelectron yields, thereby characterizing their performance limits for future high-granularity electromagnetic calorimeters.

The Gist

Imagine you are trying to build a super-precise scale to weigh everything from a single feather to a heavy truck. Now, imagine that scale is made of tiny, sensitive light-sensors called SiPMs (Silicon Photomultipliers), and instead of weighing objects, it's "weighing" particles of light (photons) created when high-energy particles crash into special crystals.

This paper is about testing how well these light-sensors handle the "heavy truck" scenario without getting overwhelmed.

The Big Problem: The "Crowded Room" Effect

Think of a SiPM like a room filled with thousands of tiny light switches (called pixels). When a particle hits a crystal, the crystal flashes with light. Each flash trips a switch.

• The Good News: If only a few people (photons) enter the room, every switch gets tripped, and we can count them perfectly.
• The Bad News: If a million people rush in at once, the room gets so crowded that some switches get tripped twice before they can reset, or they just get stuck. The room can't count everyone accurately. This is called non-linearity or saturation.

For future particle colliders (like a giant race track for atoms), scientists need to measure particles with energies up to 180 GeV. This creates a massive flood of light that could easily "choke" the sensors.

The Experiment: The "Two-Camera" Trick

To test this, the researchers built a clever setup using two cameras (sensors) on opposite ends of a long crystal bar:

1. The "Reference" Camera (SiPMRef): This one looks at the light through a pair of sunglasses (a neutral-density filter) that blocks 99% of the light. It sees a manageable amount of light, so it stays accurate and tells the team exactly how much energy was deposited.
2. The "Test" Camera (SiPMDUT): This one looks at the light with no sunglasses. It gets blasted with the full intensity.

By comparing the "Reference" (which knows the true answer) with the "Test" (which is struggling), the team could see exactly how much the Test camera was lying about the number of photons it saw.

The Setup: Making the Light Flood

To make the light flood intense enough to test the limits, they did three things:

• High-Speed Bullets: They used a beam of electrons moving at nearly the speed of light (300 GeV).
• The "Pre-Shower" Wall: Before the particles hit the crystal, they smashed into a thin sheet of Tungsten. This is like throwing a rock into a pile of sand; it creates a spray of smaller particles (a shower) that spreads out and hits the crystal with much more force.
• The Angle: They tilted the crystal so the particles traveled a longer path through it, creating even more light.

The Crystal Choice: Slow vs. Fast

They tested two types of crystals:

• BGO (Bismuth Germanate): Think of this as a slow-release light bulb. It glows for a long time (300 nanoseconds). Because the light comes out slowly, the tiny switches in the sensor have time to reset between flashes. This helps the sensor handle more light than it theoretically should.
• BSO (Bismuth Silicate): Think of this as a strobe light. It flashes very quickly (100 nanoseconds). The switches don't have time to reset, so the sensor gets confused much faster.

What They Found

1. The "Slow" Crystal Saved the Day: When using the slow BGO crystal, the sensors could handle a huge amount of light (500,000 photons) before getting about 20% confused. The "slow release" gave the sensors a chance to catch their breath.
2. The "Fast" Crystal Was Tougher: With the fast BSO crystal, the sensors got confused much earlier (about 32% error at the same light level).
3. The "NDL" Sensors Struggled: They tested some sensors from a different manufacturer (NDL) that were supposed to be better. Surprisingly, they performed worse than expected, getting confused by over 50% of the light. The team suspects these specific sensors might have some internal "glitches" or dead spots.

Why Does This Matter?

Future particle factories (like the CEPC in China) need to measure the energy of particles with extreme precision to discover new physics. If the sensors get "confused" by too much light, the measurements will be wrong.

This paper proves that:

• Pixel recovery matters: The fact that the crystals glow slowly actually helps the sensors work better than we thought.
• We can fix the math: By understanding exactly how the sensors get confused, scientists can write computer code to correct the data later, ensuring the final measurements are accurate even when the sensors are overwhelmed.

In short: The researchers built a "stress test" for light sensors, proving that while they can get overwhelmed by a massive flood of light, the specific type of crystal they are attached to can act like a shock absorber, helping them survive the crash.

Technical Summary

Here is a detailed technical summary of the paper "SiPM non-linearity studies in beam tests with scintillating crystals."

1. Problem Statement

Future $e^+e^-$ Higgs factories (e.g., CEPC) require high-granularity homogeneous electromagnetic calorimeters capable of measuring energies from minimum ionizing particles (MIPs) up to $\sim$180 GeV with percent-level energy resolution.

• The Challenge: Silicon Photomultipliers (SiPMs) are the preferred photosensors due to their compactness and magnetic field compatibility. However, SiPMs have a finite number of microcells (pixels). When the incident light intensity approaches the total pixel count, the device response becomes intrinsically non-linear due to saturation.
• The Gap: While non-linearity is well-studied for fast scintillators in medical imaging, the specific regime of high-pixel-density SiPMs (6–10 $\mu$m pitch) coupled to slow scintillators (BGO, BSO) in a collider environment has not been systematically explored. The slow decay times of these crystals ($\sim$300 ns for BGO) allow for "pixel recovery" (microcells recharging and firing again within a single pulse), a mechanism that may extend the dynamic range beyond the nominal pixel count but requires validation under realistic beam conditions.

2. Methodology

The authors conducted a dedicated beam test at the CERN SPS H2 beamline using 300 GeV electrons and 160 GeV pions.

Experimental Setup

• Dual-End Readout Scheme: A crystal bar was read out at both ends.
  • SiPM$_{DUT}$ (Device Under Test): Coupled directly to the crystal via silicone oil to receive full, unattenuated light.
  • SiPM$_{Ref}$ (Reference): Coupled to the opposite end with a Neutral Density (ND) filter (1% transmittance) to ensure it operates strictly within its linear response region.
• Energy Maximization: To push the SiPMs deep into the non-linear regime, the experiment utilized:
  • A Tungsten pre-shower plate (optimized via Geant4 simulation) to initiate electromagnetic showers upstream.
  • Variable incident angles: Rotating the crystal relative to the beam to increase the effective path length of the shower, achieving energy depositions $>100$ GeV.
• Components Tested:
  • Crystals: BGO (40 cm and 12 cm) and BSO (12 cm).
  • SiPMs: Hamamatsu (S14160-3010PS and S14160-6010PS) and NDL (EQR06 and EQR10) with pixel pitches ranging from 6 to 10 $\mu$m.
• Calibration Chain:
  1. Pre-amplifier Calibration: Charge injection to correct non-linearities in the electronics.
  2. SiPM Gain Calibration: Using LED pulses to determine single-photoelectron (p.e.) gain (extrapolated from low-temperature measurements where necessary).
  3. MIP Calibration: Using 160 GeV pions to establish the energy-to-signal conversion factor.
  4. Relative Light Collection Efficiency (RLCE): Using the linear SiPM$_{Ref}$ signal to calibrate the expected response of SiPM$_{DUT}$ in the absence of saturation.

3. Key Contributions

• First Systematic Beam Test: This is one of the first studies to quantify SiPM non-linearity driven by scintillation light in a realistic high-energy beam environment, rather than just benchtop laser tests.
• Dual-End Calibration Technique: The authors developed a robust method using an attenuated reference SiPM to precisely calibrate the deposited energy and photon count over an ultra-wide dynamic range (up to $5 \times 10^5$ p.e.).
• Quantification of Pixel Recovery: The study explicitly demonstrates how the slow decay time of BGO/BSO crystals facilitates pixel recovery, effectively extending the dynamic range beyond the static microcell count.
• Comparative Analysis: Provided a direct comparison between different crystal lengths, scintillator types (BGO vs. BSO), and SiPM manufacturers (Hamamatsu vs. NDL).

4. Key Results

• Non-Linearity in Hamamatsu SiPMs:
  • For BGO-coupled Hamamatsu SiPMs, deviations from linearity were observed to be approximately 20% at $5 \times 10^5$ photoelectrons.
  • The 6 mm and 3 mm Hamamatsu devices showed similar saturation behaviors despite different pixel densities, suggesting a balance between photon density and junction capacitance effects.
• Impact of Scintillator Decay Time:
  • BSO (Faster decay): Exhibited significantly stronger non-linearity (-32.2%) compared to BGO. The faster decay leads to higher instantaneous pixel occupancy, reducing the benefit of pixel recovery.
  • Crystal Length: Results from 12 cm and 40 cm BGO crystals were nearly identical, indicating that intrinsic scintillation decay time dominates non-linearity, while photon transport time differences due to crystal length are negligible.
• NDL SiPM Performance:
  • NDL devices showed unexpectedly poor performance, with non-linearity deviations exceeding 50% (up to -66.9% for EQR10) at $5 \times 10^5$ p.e.
  • This contradicts theoretical expectations based on their smaller junction capacitance and faster recovery times. The authors suggest device-specific defects (e.g., non-functional pixels or gain variations under high load) as potential causes.
• Systematic Uncertainties: The total systematic uncertainty for the measurements was determined to be within 3%, dominated by pre-amplifier calibration and crystal non-uniformity.

5. Significance

• Validation for Future Detectors: The results confirm that BGO/BSO-SiPM systems are viable for Higgs factory calorimetry, as the pixel recovery effect mitigates saturation, allowing for a dynamic range sufficient to measure high-energy showers.
• Correction Models: The data provides a benchmark for developing non-linearity correction models. It highlights that models developed for fast scintillators cannot be directly applied to slow scintillators like BGO.
• Technology Selection: The study identifies that while Hamamatsu SiPMs perform as expected, NDL devices in this specific configuration require further investigation before deployment in high-precision calorimeters.
• Methodological Framework: The dual-end readout and calibration strategy presented offers a reproducible framework for characterizing future SiPM-based detectors in high-granularity calorimetry.