Identification and simulation of surface alpha events on passivated surfaces of germanium detectors and the influence of metalisation

This paper investigates alpha-induced surface events on passivated germanium detectors by analyzing charge trapping effects, verifying pulse-shape identification techniques, discovering a novel dependence on crystal axes, and introducing a simulation model within SolidStateDetectors.jl to better understand background contributions in neutrinoless double-beta decay searches.

The Gist

Imagine you are trying to listen for a single, perfect whisper in a very noisy room. That whisper is a rare event in physics called "neutrinoless double-beta decay," which could help us understand why the universe exists. To hear it, scientists use giant, ultra-pure Germanium crystals that act like incredibly sensitive microphones.

However, there's a problem: the room isn't just noisy; it's full of people shouting right next to the microphone. These "shouts" are alpha particles hitting the surface of the crystal. Because they hit the edge, they get muffled and distorted, making them sound like the whisper we are looking for. This creates a false alarm.

This paper is about learning exactly how these surface shouts get distorted so scientists can filter them out and finally hear the whisper.

Here is the story of their investigation, broken down into simple concepts:

1. The Crystal and the "Dead Zone"

Think of the Germanium detector as a giant, hollow cylinder (like a toilet paper roll made of super-pure ice). The inside is the "active zone" where the magic happens. The outside is covered in a protective skin called a passivated surface.

When an alpha particle (a tiny, heavy bullet) hits this skin, it doesn't penetrate deep. It stops almost immediately. As it tries to move through the crystal to create a signal, it gets stuck.

• The Analogy: Imagine walking through a crowded hallway. If you are in the middle, you walk straight to the exit. But if you are right at the wall, people (impurities) grab your coat, trip you, or slow you down. You still get to the exit, but you arrive late and tired. In the detector, this "tiredness" means the energy signal is weaker and looks different than a real event.

2. The "Mirror" Effect

The detector is divided into 19 slices (like cutting a pizza into 19 pieces). When an alpha particle hits the top slice (Segment 19), it usually gets stuck before reaching the center.

• The Analogy: Imagine you are pushing a heavy box across a floor. If you push it from the top, the floor underneath vibrates. The scientists noticed that when the top slice gets a "muffled" signal, the slices underneath it show a weird, "truncated" echo. They call these mirror pulses.
• The Discovery: By looking at these mirror pulses, the team realized they could tell exactly where the particle got stuck. If the signal is weird on the top and echoes weirdly on the bottom, they know, "Aha! This is a surface event, not the rare whisper we want!"

3. The Crystal's "Highways" and "Backroads"

Germanium crystals aren't perfectly uniform; they have a specific internal structure (like a grid). The scientists discovered something new: the direction you walk matters.

• The Analogy: Imagine the crystal has "Fast Lanes" (Fast Axes) and "Slow Lanes" (Slow Lanes).
  • If an electron tries to move along a Fast Lane, it zooms through quickly and gets stuck less.
  • If it tries to move along a Slow Lane, it gets bogged down in traffic and gets stuck more often.
• The Result: The team found that alpha particles hitting the crystal at different angles (rotating around the cylinder) produced different amounts of "muffling." This was the first time anyone saw this specific "traffic jam" effect depend on the crystal's internal direction.

4. The "Metal Coat" Experiment

The detector's segments were originally only partially covered in metal (like a jacket with only the shoulders covered). Later, they covered the whole thing in metal (a full jacket).

• The Analogy: Think of the metal coating as a smooth, slippery slide.
  • Partial Metal: If you only have a slide on one side, people get stuck on the rough wood on the other side. The signals were very messy and depended heavily on where you stood.
  • Full Metal: Once they covered the whole thing in metal, the "slide" was smooth everywhere. The signals became much cleaner and faster, regardless of where the particle hit.
• The Lesson: How you coat the detector changes how the signals behave. A full metal coat makes it much easier to tell the difference between a surface event and a real event.

5. Building a "Video Game" of the Crystal

To prove their theories, the scientists built a computer simulation (a video game) using open-source software called SolidStateDetectors.jl.

• They created a virtual crystal and programmed "rules" for how particles get stuck (trapped) based on the dead layer, the surface, and the probability of getting caught.
• The Outcome: The simulation matched their real-world data almost perfectly. They could now predict exactly how much energy would be lost based on where the particle hit and which "lane" it was in.

Why Does This Matter?

The LEGEND experiment (the next big step in this research) is currently being built underground to hunt for that rare "whisper" (neutrinoless double-beta decay).

• If they can't filter out the "shouts" from the surface, they will never hear the whisper.
• This paper gives them the filter. It tells them: "If the pulse looks like this (slow tail, weird mirror echo), it's a surface event. Throw it away. If it looks like that, it might be the real thing."

In short: The scientists mapped out the "traffic jams" inside their giant crystal, figured out how the crystal's internal roads affect the traffic, and proved that giving the crystal a full metal coat makes the traffic flow much better. This allows them to build a better filter to find the most important secrets of the universe.

Technical Summary

1. Problem Statement

High-purity germanium (HPGe) detectors are critical for rare-event searches, such as neutrinoless double-beta decay ($0\nu\beta\beta$) in $^{76}$Ge (e.g., the LEGEND experiment). A major background source in these searches arises from alpha interactions on the passivated surfaces of the detectors.

• The Issue: Alpha particles interacting near the surface suffer from charge trapping (electrons or holes getting trapped in crystal defects before reaching the electrodes).
• Consequence: This trapping reduces the observed energy of the event. If the energy loss is significant, the alpha event can be misreconstructed to fall within the Region of Interest (ROI) around the $Q$-value of the decay ($2039$ keV), mimicking a signal event.
• Knowledge Gap: While pulse-shape discrimination (PSD) is used to reject surface events, a detailed understanding of the charge trapping mechanisms, their dependence on crystal orientation, and the influence of detector metallization (contact coating) was lacking.

2. Methodology

The study utilized the GALATEA test facility at the Max Planck Institute for Physics, featuring a vacuum chamber with motorized stages to scan a detector surface with alpha sources.

• Detector: The "Super-Siegfried" detector, a segmented, true-coaxial, n-type HPGe detector. It features a central core contact and 19 segmented p+ contacts on the outer mantle.
  • Unique Feature: Segment 19 (top end-plate) is thin and designed to study passivated surface events. It generates "mirror pulses" in the segments underneath (9 and 10), aiding in detailed pulse analysis.
  • Configuration: The study compared data taken when Segment 19 was partially metalised (only near the readout cable) versus fully metalised.
• Sources: Two open $^{241}$Am sources ($74$ kBq each) were used to irradiate the detector side and top simultaneously. $^{241}$Am emits alpha particles ($\sim 5.4$ MeV) and $59.5$ keV gammas.
• Data Acquisition:
  • Scans included radial scans along fast ($\langle 100 \rangle$) and slow ($\langle 110 \rangle$) crystal axes, and rotational (azimuthal) scans.
  • Raw pulses were recorded at $250$ MHz.
  • Event Selection: A two-step cut was applied:
    1. S-cut: $E_{19} > \sum_{i=1}^{18} E_i$ (selects events where the top segment collects the most energy, filtering out side gammas).
    2. $\tau$-cut: Selection based on the decay constant ($\tau$) of the pulse tail. Alpha events on passivated surfaces exhibit positive tail slopes (increased effective $\tau$) due to slow release of trapped charge or low mobility near the surface, distinguishing them from bulk events.
• Simulation: The open-source package SolidStateDetectors.jl (SSD) was used to model the detector. A new physics model was introduced to simulate surface effects, including:
  1. A radius-dependent dead layer.
  2. A surface channel (virtual volume) where charge carrier drift is modulated to run parallel to the surface.
  3. Probabilistic charge trapping for electrons and holes within this surface channel.

3. Key Contributions

• First Observation of Crystal Axis Dependence: The study demonstrated for the first time that the probability of charge trapping depends on the crystal orientation. Events near the fast axis ($\langle 100 \rangle$) showed less trapping (higher reconstructed energy) than those near the slow axis ($\langle 110 \rangle$), attributed to higher carrier mobility along the fast axis.
• Validation of PSD Technique: The study verified that analyzing the tail slope of the core pulse is an effective method to identify and select alpha events affected by charge trapping, even when they appear as multi-segment events due to mirror pulses.
• New Simulation Framework: A comprehensive model was developed within SSD to describe surface charge trapping, incorporating a dead layer, surface channel drift modulation, and probabilistic trapping.
• Metallization Impact: The study quantified the effect of full vs. partial metallization on pulse shapes, specifically rise times.

4. Key Results

• Charge Trapping Characteristics:
  • Radial Dependence: Small radii (closer to the core) are dominated by hole trapping; large radii (closer to the mantle) are dominated by electron trapping. This correlates with the drift path length to the respective collecting electrode.
  • Trapping Probability: The probability of trapping per unit time/distance was found to be approximately 3 times higher for electrons than for holes directly under the passivated top surface.
  • Energy Reduction: Trapping causes observed energies to drop from the expected $\sim 5.4$ MeV to a broad distribution around $2$ MeV, overlapping with the $0\nu\beta\beta$ signal region.
• Simulation Performance:
  • The SSD model successfully reproduced the radial dependence of the observed energies ($E_0$ and $E_{19}$) and the correlation between core and segment energies.
  • The model suggested a dead layer thickness increasing from $\sim 8$ $\mu$m at the center to $\sim 12$ $\mu$m at the edge.
  • The simulation reproduced the "half-moon" shape of energy correlations at medium radii (though the beam-spot spread was not fully modeled).
• Influence of Metallization:
  • Partial Metallization: Previously, events near the top surface showed extremely long rise times ($\sim 730$ ns variation) and strong dependence on the azimuthal angle relative to the readout contact.
  • Full Metallization: After full metalization, rise times became significantly faster and more uniform. The dependence on the readout position was drastically reduced (variation dropped to $\sim 70$ ns), and the modulation due to crystal axes became visible again.
  • Implication: Full metallization stabilizes the electric field near the surface, reducing the "slow" pulse components caused by surface charge accumulation.

5. Significance

• Background Suppression for LEGEND: The findings confirm that surface alpha events can be efficiently identified and rejected using pulse-shape analysis (specifically tail slope and mirror pulse signatures). This is crucial for the LEGEND experiment to achieve its goal of increasing sensitivity to $0\nu\beta\beta$ decay.
• Detector Design Optimization: The study highlights that the metallization scheme significantly impacts pulse shapes. Full metalization is shown to reduce pulse shape distortions and position-dependent variations, suggesting that future detector designs should prioritize full surface coverage to minimize surface-related backgrounds.
• Simulation Advancement: The integration of surface trapping physics into SolidStateDetectors.jl provides a powerful tool for future detector simulations, allowing for more accurate background modeling and optimization of detector geometries and readout strategies.
• Fundamental Physics: The observation of crystal-axis-dependent trapping provides new insights into charge carrier transport near semiconductor surfaces, linking macroscopic pulse shapes to microscopic crystal properties.