Proton Energy Dependence of Radiation Induced Low Gain Avalanche Detector Degradation

This study demonstrates that while lower-energy protons generally cause more severe degradation in Low Gain Avalanche Detectors (LGADs) due to acceptor removal, 400 MeV protons exhibit unexpectedly lower damage than both lower and higher energies, revealing that standard 1 MeV neutron-equivalent fluence scaling fails to fully capture the complex, non-monotonic energy dependence of radiation-induced defect formation.

The Gist

Imagine you are building a high-speed camera for a particle collider. To capture the split-second moments when particles collide, you need sensors that can "see" incredibly fast. The paper discusses a special type of sensor called an LGAD (Low Gain Avalanche Detector).

Think of an LGAD as a highly sensitive microphone inside a noisy room. To hear a whisper (a single particle), the microphone has a built-in amplifier (the "gain layer") that boosts the signal. However, this amplifier is made of a very delicate material. Over time, the "noise" of the particle collider (radiation) damages this amplifier, making it harder to hear the whispers. Eventually, the microphone stops working.

The scientists wanted to know: Does the "loudness" or "type" of the radiation matter? Specifically, they tested how different speeds of protons (tiny subatomic particles) damage these sensors.

The Experiment: A Race Against Radiation

The researchers took these sensors from two different manufacturers (HPK and CNM) and blasted them with protons at four very different speeds:

1. Slow: 18 and 24 MeV (Mega-electronvolts)
2. Medium-Fast: 400 MeV
3. Super Fast: 23 GeV (Giga-electronvolts)

They hit the sensors with varying amounts of these particles, simulating years of wear and tear in a single experiment.

The Surprising Findings

Usually, scientists assume that if you know how many particles hit a sensor, you can predict the damage using a standard rulebook (called NIEL scaling). It's like assuming that hitting a wall with 100 small pebbles causes the same damage as hitting it with 100 large boulders, as long as you adjust for weight.

The paper found that this rulebook is wrong.

Here is what they discovered, using simple analogies:

• The Slow Protons (18–24 MeV) are the "Brute Force" Destroyers:
  These slow-moving particles caused the most damage. Imagine a sledgehammer hitting a glass window. Even though it's moving slowly, it creates huge, messy cracks that destroy the amplifier immediately. The sensors lost their ability to boost signals very quickly.

• The Super Fast Protons (23 GeV) are the "Sniper":
  These incredibly fast particles caused moderate damage. They are like a high-speed bullet. They punch through cleanly but still cause significant structural issues. The sensors degraded, but not as instantly as with the slow ones.

• The Medium-Fast Protons (400 MeV) are the "Mystery Anomaly":
  This is the most surprising part. The 400 MeV protons caused the least damage of all.

  • The Analogy: Imagine you are trying to break a vase. You hit it with a slow sledgehammer (18 MeV) and it shatters. You hit it with a supersonic bullet (23 GeV) and it cracks badly. But when you hit it with a medium-speed rock (400 MeV), the rock seems to bounce off or slide through without breaking the glass as much as the others.
  • The sensors hit by these particles kept working much longer than expected, even longer than those hit by the super-fast protons.

Why Does This Matter?

The scientists tried to use the standard "rulebook" (NIEL scaling) to fix the data. They converted all the different proton speeds into a common unit (like converting miles and kilometers into "standard damage units").

The rulebook failed again. Even after doing the math to make them "equal," the 400 MeV protons still looked much less harmful than the others.

This tells us that the "damage" isn't just about how much energy is dumped into the sensor. It's about how that energy is delivered.

• Slow protons seem to create a specific type of damage (like scattered, messy defects) that kills the sensor fast.
• 400 MeV protons seem to create a different kind of damage that the sensor can survive better.

The Carbon Twist

The researchers also tested sensors with a special ingredient added: Carbon.

• The Analogy: Think of the sensor material as a sponge. Adding carbon is like reinforcing the sponge with steel fibers.
• Result: The carbon-reinforced sensors held up much better against the "slow sledgehammer" protons. The carbon acted as a shield, slowing down the rate at which the amplifier broke.

The Bottom Line

This paper is a warning to engineers building future particle detectors. You cannot just assume that "more radiation equals more damage" in a straight line. The speed of the radiation particles changes the type of damage they do.

Specifically, the "medium-fast" protons (400 MeV) are surprisingly gentle on these sensors, while the "slow" ones are surprisingly brutal. This means the current models used to predict how long these sensors will last need to be rewritten to account for these weird energy levels.

Technical Summary

Technical Summary: Proton Energy Dependence of Radiation Induced Low Gain Avalanche Detector Degradation

Problem Statement
Low Gain Avalanche Detectors (LGADs) are critical for precision timing in high-energy physics, particularly for the High-Luminosity LHC (HL-LHC) upgrades. Their performance relies on a p+ gain layer that facilitates controlled charge multiplication via impact ionization. However, this layer is susceptible to radiation-induced degradation, primarily through "acceptor removal," which leads to a loss of gain and timing resolution. While radiation damage is typically quantified using Non-Ionizing Energy Loss (NIEL) scaling to relate different particle types and energies, simulations suggest that proton energy qualitatively alters defect structures (e.g., point defects vs. clustered defects). Previous studies indicate that low-energy hadrons may degrade LGADs faster than neutrons of comparable fluence, suggesting that standard NIEL scaling may be insufficient for predicting degradation across a broad hadron energy spectrum.

Methodology
The study conducted a systematic comparison of LGAD degradation using devices from two manufacturers: Hamamatsu Photonics (HPK) and the Institute of Microelectronics of Barcelona (IMB-CNM).

• Devices: HPK devices from prototype wafers W25 and W36, and CNM devices (W1, W2, W4) with varying levels of carbon enrichment in the gain layer.
• Irradiation: Samples were irradiated with protons at four distinct energies: 18 MeV, 24 MeV, 400 MeV, and 23 GeV. Fluences ranged up to $2.5 \times 10^{15} \text{ p/cm}^2$.
• Characterization:
  • Electrical: Current-Voltage (I-V) and Capacitance-Voltage (C-V) measurements were performed to determine the gain layer depletion voltage ($V_{gl}$) and breakdown voltage ($V_{break}$). These were used to extract acceptor removal coefficients ($c$).
  • Laser (TCT): Infrared Transient Current Technique (TCT) measurements were performed on HPK devices to assess charge collection and gain evolution, calculating gain by comparing collected charge to reference diodes.
• Analysis: Proton fluences were converted to 1 MeV neutron-equivalent fluences ($\Phi_{eq}$) using standard hardness factors to test the validity of NIEL scaling.

Key Results

1. Energy Dependence of Degradation: The study confirmed that lower energy protons induce stronger gain layer degradation. The acceptor removal coefficients were highest for 18 MeV and 24 MeV protons, indicating the fastest loss of gain.
2. Non-Monotonic Behavior at 400 MeV: A significant and unexpected finding is that 400 MeV protons consistently caused less damage than both lower (18–24 MeV) and higher (23 GeV) energy protons. This deviation from a monotonic energy trend was observed across all device types (HPK and CNM) and remained evident even after converting fluences to neutron equivalents.
3. Limitations of NIEL Scaling: Converting proton fluences to 1 MeV neutron equivalents reduced the spread in degradation data but did not eliminate the differences between energy groups. Specifically, the 400 MeV data still showed the weakest degradation. This indicates that standard NIEL scaling does not fully account for the underlying defect formation mechanisms across different proton energies.
4. Carbon Mitigation: For CNM devices, carbon implantation in the gain layer was shown to mitigate acceptor removal, with higher carbon doses resulting in systematically smaller removal coefficients.
5. Gain Evolution: Laser characterization corroborated electrical findings. While 23 GeV and 400 MeV protons showed similar gain evolution at low fluences, 23 GeV devices experienced rapid gain loss at higher fluences ($>5 \times 10^{14} \text{ neq/cm}^2$), whereas 400 MeV devices retained measurable gain up to $\approx 10^{15} \text{ neq/cm}^2$. Conversely, 24 MeV protons caused the most rapid gain reduction.

Significance and Claims
The paper asserts that the observed non-monotonic energy dependence, particularly the reduced damage from 400 MeV protons compared to 23 GeV protons, challenges the sufficiency of the standard NIEL framework for LGADs. The authors claim that the current scaling model fails to distinguish between different defect formation mechanisms (such as point defects versus clusters) that vary with incident energy. Consequently, the study suggests that NIEL scaling requires revision to ensure reliable sensor performance in complex irradiation fields containing a broad spectrum of particle types and energies. The work provides a quantitative basis (acceptor removal coefficients) for future simulations and modeling efforts aimed at refining radiation hardness predictions for LGADs.