In-Situ Performance of FBK VUV-HD3 and HPK VUV4 SiPMs in the LoLX Liquid Xenon Detector

This paper presents a direct in-situ comparison of FBK VUV-HD3 and HPK VUV4 SiPMs within the LoLX liquid xenon detector, revealing that HPK devices detect 33–38% less light than FBK devices under operating conditions and demonstrating that this discrepancy is resolved by an optical simulation incorporating angular and wavelength-dependent surface shadowing effects.

The Gist

The Great Light Catch-Off: A Tale of Two Sensors in a Frozen Sea

Imagine you are trying to catch fireflies in a dark, frozen room. To do this, you have built a small, transparent box filled with liquid that acts like a giant mirror for light. When a tiny particle (like a ghostly dark matter particle) bumps into this liquid, it flashes a tiny burst of ultraviolet light—so faint that you need incredibly sensitive "eyes" to see it.

In the world of physics, these "eyes" are called SiPMs (Silicon Photomultipliers). They are the cameras of the future for detecting the universe's most elusive secrets.

This paper is about a race between two different brands of these "eyes":

1. FBK (The Flat Catcher): A sensor with a smooth, flat surface.
2. HPK (The Recessed Catcher): A sensor with a little "bowl" or recessed window inside its casing.

The scientists wanted to know: Which one catches more light when they are both sitting inside a tank of liquid xenon?

The Setup: The LoLX Tank

The researchers built a small, 4-centimeter cube filled with liquid xenon (which is basically super-cold, heavy fog). They lined the walls of this cube with 40 FBK sensors and 40 HPK sensors, all staring at the same space. They then shot gamma rays (invisible energy beams) from outside the tank to make the liquid xenon flash.

Think of it like shining a flashlight into a room full of mirrors and asking, "How much light does each mirror reflect back to me?"

The Surprise: The "Bowl" Problem

The scientists expected the two sensors to perform somewhat similarly, based on how they looked in a vacuum (empty space). But when they turned on the lights in the liquid xenon, the results were shocking.

The HPK sensors (the ones with the "bowl") only caught about 65% of the light that the FBK sensors (the flat ones) caught.

That's a huge difference! It's like if you and a friend were trying to catch rain with buckets, and your friend's bucket was 35% smaller than yours, even though they claimed their bucket was just as good.

Why Did This Happen? The "Doorway" Analogy

The scientists dug deeper to find out why. They realized the problem wasn't just the sensor itself, but how the light arrived.

Imagine the light particles (photons) are like people trying to enter a room.

• The FBK Sensor is like a wide-open door on a flat wall. People can walk in from almost any angle.
• The HPK Sensor is like a door set deep inside a hallway with high walls (the ceramic package).

In the liquid xenon tank, the light doesn't just come straight at the sensors; it bounces around and hits them from weird, sideways angles (grazing angles).

• When light hits the FBK flat sensor from the side, it slides right in.
• When light hits the HPK recessed sensor from the side, it hits the "walls" of the ceramic package first. The light gets blocked or reflected away before it ever reaches the sensor inside the "bowl."

The scientists called this "Shadowing." The HPK sensor's own packaging was casting a shadow over itself, blocking the light that came in at an angle.

The Solution: A Better Map

The researchers built a super-computer simulation (a digital twin of their experiment) to prove this.

• Old Model: They first tried a model that assumed light only came straight on. This model predicted the sensors would be almost equal. It was wrong.
• New Model: They added the "shadow" effect to the simulation. They told the computer, "Hey, remember the HPK sensor has a bowl, and light hitting it from the side gets blocked."

Suddenly, the computer's prediction matched the real-world experiment perfectly! The simulation showed that because of the "bowl" shape, the HPK sensors naturally lose a lot of light in this specific setup.

What Does This Mean for the Future?

This paper teaches us a very important lesson for building giant detectors (like the ones used to hunt for Dark Matter):

You can't just look at a sensor's specs in a vacuum.
A sensor might look amazing in a lab test where light hits it straight on. But inside a real detector, light comes from all directions. If you put a sensor with a "bowl" in a place where light hits it from the side, it will underperform.

The Takeaway:
When designing the next generation of giant, deep-space detectors, scientists must be careful about the shape of the sensor's packaging. They need to simulate how light bounces around the whole room, not just how the sensor works in isolation.

In short: Don't judge a fish by its ability to climb a tree, and don't judge a light sensor by how it performs in a straight line. The shape of the sensor matters just as much as the sensor itself.

Technical Summary

1. Problem Statement

Silicon Photomultipliers (SiPMs) are critical for next-generation liquid xenon (LXe) detectors used in rare-event searches (e.g., dark matter, neutrinoless double beta decay). While two leading manufacturers, Fondazione Bruno Kessler (FBK) and Hamamatsu Photonics (HPK), produce VUV-sensitive SiPMs, there is a lack of comprehensive in-situ comparative data in liquid xenon environments.

• The Discrepancy: Vacuum measurements and standard Photon Detection Efficiency (PDE) models suggest HPK and FBK devices should perform similarly (with HPK having a slightly lower fill factor). However, preliminary in-situ data suggested HPK devices were significantly less efficient than predicted.
• The Gap: Existing studies lacked direct, simultaneous comparison of FBK VUV-HD3 and HPK VUV4 SiPMs under identical operating conditions, and standard models often fail to account for complex geometric and angular effects in real detector volumes.

2. Methodology

The authors conducted a direct comparison using the LoLX 2 (Light-only Liquid Xenon) detector, a 4 cm cubic vessel containing ~5 kg of LXe.

• Detector Configuration:
  • The detector features a modular design with five faces instrumented with SiPMs and a sixth face with a PMT for triggering.
  • Sensor Layout: 40 FBK VUV-HD3 and 40 HPK VUV4 SiPMs were installed (4×4 arrays per tile).
  • Geometry Differences: FBK devices have a flat topology, while HPK devices feature a recessed window within a ceramic package.
• Data Acquisition:
  • Sources: External gamma sources ($^{133}$Ba at ~356 keV and $^{137}$Cs at 662 keV) were used to generate scintillation light.
  • Calibration: Single Photoelectron (SPE) calibration was performed using an external visible laser to determine channel gains and thresholds.
  • Signal Processing: A pulse-finding algorithm was used. For events saturating the digitizer (due to high photon flux), a custom pulse-fitting algorithm based on a modified Single Avalanche Response Function (SARF) was applied to reconstruct true pulse amplitudes.
• Simulation Framework:
  • A multi-stage pipeline was developed: Geant4 (particle interactions) $\rightarrow$ NEST (scintillation yield) $\rightarrow$ Chroma (GPU-accelerated optical photon transport).
  • PDE Model: The simulation utilized an advanced, angular- and wavelength-dependent PDE model (Ref. [17]) that includes:
    • Fill factor ($FF$).
    • Wavelength ($\lambda$) and Angle of Incidence (AOI, $\theta$) dependent transmission ($T$) and specular reflectivity ($R_{sp}$).
    • Crucial Addition: A "surface shadowing" correction factor specifically for the HPK recessed package geometry, which blocks photons arriving at grazing angles.

3. Key Contributions

• First Direct In-Situ Comparison: Provided the first simultaneous, side-by-side performance comparison of FBK VUV-HD3 and HPK VUV4 SiPMs in a liquid xenon environment.
• Resolution of Efficiency Discrepancy: Demonstrated that the observed ~33–38% lower light collection for HPK devices is not due to intrinsic sensor failure but is a result of geometric shadowing and angular dependence.
• Validation of Advanced Optical Modeling: Proved that standard vacuum-based PDE models are insufficient for LXe detector design. Accurate predictions require integrating angular-dependent PDE with macroscopic geometric transport effects (package shadowing).

4. Results

• Experimental Ratios:
  • The HPK-to-FBK photon detection ratio was measured to be 0.62 ($^{133}$Ba) and 0.67 ($^{137}$Cs).
  • This indicates HPK devices detect 33–38% less light than FBK devices under these specific conditions.
• Simulation vs. Experiment:
  • Without Shadowing: A simulation ignoring the HPK package geometry predicted a ratio of ~0.68–0.71, which significantly overestimated HPK performance compared to data.
  • With Shadowing: When the simulation included the angular-dependent PDE model and the geometric shadowing of the HPK recessed window, the predicted ratios dropped to 0.63 ($^{133}$Ba) and 0.66 ($^{137}$Cs).
  • Agreement: The shadowing-inclusive simulation matched the experimental data within statistical uncertainties ($<0.2\sigma$).
• Mechanism of Loss:
  • The HPK ceramic package and recessed window block a significant portion of photons arriving at large angles (grazing incidence), which are common in a cubic detector geometry.
  • The FBK flat topology allows for better acceptance of these grazing photons.
  • The difference in energy between $^{133}$Ba and $^{137}$Cs sources resulted in slightly different ratios because higher-energy gammas ($^{137}$Cs) produce a more uniform spatial distribution of light, leading to a slightly higher average angle of incidence (closer to normal) and thus a higher effective ratio.

5. Significance and Implications

• Detector Design: Future large-scale LXe detectors cannot rely solely on normal-incidence vacuum PDE specifications. The effective efficiency is a convolution of intrinsic sensor properties and the specific detector geometry.
• Modeling Requirements: Robust performance predictions for rare-event searches require full optical simulations that incorporate:
  1. Angular-dependent PDE.
  2. Wavelength-dependent optical properties.
  3. Macroscopic geometric shadowing effects (e.g., ceramic packages, recessed windows).
• Technology Selection: While FBK VUV-HD3 shows superior light collection in this specific cubic geometry due to its flat profile, the study validates that HPK VUV4 performance can be accurately predicted if the correct geometric models are applied. This allows for informed trade-offs between sensor types based on specific detector layouts.

In conclusion, the paper establishes that the "missing" light in HPK SiPMs is a geometric artifact of the detector environment, not a fundamental sensor defect, and provides a validated framework for modeling these effects in future experiments.