Characterization of afterpulse in SiPMs with single-cell readout as a function of bias voltage and fluence

This study utilizes a single-cell readout SiPM structure and three validated analysis methods to demonstrate that afterpulse probability and time constants remain largely independent of neutron irradiation fluence, with probabilities below 6% and time constants under 10 ns for overvoltages between 3 and 5 V.

The Gist

Imagine you have a very sensitive microphone designed to hear a single whisper in a quiet room. In the world of physics, this microphone is called a Silicon Photomultiplier (SiPM). It's a device used to detect tiny flashes of light (photons), which is crucial for things like medical scanners and particle accelerators.

However, these microphones aren't perfect. Sometimes, after they hear a whisper, they "echo" on their own. This is called afterpulsing. It's like when you clap your hands, and a second, fainter clap happens a split second later, even though you didn't clap again.

This paper is about investigating those unwanted "echoes" to see if they get worse when the microphones get damaged by radiation (like in space or nuclear reactors).

Here is the breakdown of their study using everyday analogies:

1. The Problem: The "Echo" in the Room

Normally, when scientists look at a whole array of these microphones (a big grid of them), it's hard to tell what's going on.

• The Noise: Sometimes the microphone hears a ghost sound because of heat (thermal noise).
• The Crosstalk: Sometimes one microphone gets so excited it accidentally triggers its neighbor (like shouting in a crowded room).
• The Afterpulse: This is the main villain. A single electron gets trapped inside the microphone's "trap" and then pops out later, creating a fake second signal.

Because all these things happen at once in a normal grid, it's like trying to hear one specific person's echo in a stadium full of people shouting. You can't tell who is making the noise.

2. The Solution: The "Soloist" Microphone

To solve this, the researchers built a special microphone where only one tiny cell (a single pixel) is wired up to listen.

• The Analogy: Imagine a choir where everyone is singing, but the researchers put a soundproof box around one singer and gave them a solo microphone. Now, they can hear only that one singer's voice and any echoes they make, without anyone else interfering.
• This allows them to study the "echo" (afterpulse) in isolation, without the confusion of neighbors triggering each other.

3. The Experiment: The "Radiation Rain"

They took three of these special solo microphones:

1. The Fresh One: A brand-new, untouched device.
2. The "Lightly Dusted" One: Exposed to a moderate amount of radiation (like a light rain of neutron particles).
3. The "Heavy Storm" One: Exposed to a massive amount of radiation (a heavy downpour).

They then fired a laser at them to create a "primary whisper" (a real signal) and watched what happened in the next microsecond. They used a super-fast camera (10 billion frames per second) to record the waveforms.

4. The Detective Work: Three Ways to Count the Echoes

The researchers developed three different math tricks to count the echoes:

• Method A (The Bucket): They just measured the total "water" (charge) in the bucket after the main splash.
• Method B & C (The Pattern Matcher): They used a smart computer algorithm (like a highly trained detective) that looks at the shape of the sound wave. It knows exactly what a single "whisper" looks like. If a tiny "echo" is hiding on the tail end of the main wave, the detective finds it and says, "Ah, there's a second pulse!"

They tested these methods using computer simulations first to make sure they weren't hallucinating the echoes.

5. The Big Discovery: The Echoes Didn't Get Worse

Here is the surprising result:

• The Expectation: Usually, when you damage a silicon chip with radiation, you create more "traps" (holes in the fabric of the material) that catch electrons. You would expect the "echoes" to get louder and more frequent as the damage increases.
• The Reality: Even after the "heavy storm" of radiation, the number of echoes and the speed of the echoes stayed exactly the same as the fresh device.
  • The Echo Speed: The echoes happened very fast (within 10 nanoseconds).
  • The Echo Count: The chance of an echo happening was less than 6%.

What Does This Mean?

The researchers concluded that the "echoes" they are seeing aren't caused by the deep, permanent damage radiation usually causes (like deep holes in the silicon). Instead, they are likely caused by:

1. Shallow Traps: Very minor, temporary glitches in the material that don't get worse with radiation.
2. Optical Tricks: Maybe the light from the first pulse is bouncing around inside the chip and triggering a second pulse, rather than a physical electron getting stuck.

The Bottom Line

If you are building a detector for a space mission or a nuclear plant, you might worry that radiation will ruin your sensor's ability to distinguish real signals from fake echoes. This paper says: "Don't worry about the echoes getting worse due to radiation, at least for the first few microseconds."

The "echoes" are a natural quirk of the device, not a sign of radiation damage. This is great news for scientists designing future experiments, as it means their sensors will remain reliable even after being bombarded by radiation.

Technical Summary

1. Problem Statement

Silicon Photomultipliers (SiPMs) are critical for high-energy physics due to their high gain and single-photon resolution. However, their performance is degraded by stochastic noise, specifically Dark Count Rate (DCR), Optical Crosstalk (CT), and Afterpulsing (AP).

• The Challenge: In standard SiPM arrays, the temporal overlap of these phenomena makes it difficult to isolate pure trap parameters. Optical crosstalk (spatial) and afterpulsing (temporal) often occur simultaneously, complicating the extraction of intrinsic device properties, particularly after irradiation.
• The Gap: There is a need to decouple spatial crosstalk from temporal afterpulsing to accurately characterize trap lifetimes and probabilities, especially under radiation damage conditions relevant to future collider experiments.

2. Methodology

The study employs a unique experimental setup and a rigorous three-stage data analysis pipeline.

A. Experimental Setup

• Device: A dedicated single-cell SiPM (Hamamatsu S14160) with an $11 \times 11$ pixel array. Crucially, the central pixel is physically decoupled with independent biasing and readout.
• Samples: Three devices were tested:
  1. A fresh, non-irradiated reference.
  2. Two irradiated samples exposed to reactor neutron fluences of $\Phi = 2 \cdot 10^{12}$ and $1 \cdot 10^{13} \text{ cm}^{-2}$.
• Conditions: Measurements were taken at overvoltages ($\Delta U$) of 2–5 V above breakdown. Waveforms were captured at 10 GS/s within a 1 $\mu$s window, synchronized to a 451 nm laser trigger. Surrounding pixels were biased below breakdown to suppress spatial crosstalk.

B. Data Analysis Pipeline
The authors developed three independent methods to quantify afterpulse events, validated by Monte Carlo (MC) simulations:

1. Pulse Identification (MLR): A Multiple Linear Regression (MLR) algorithm models the raw waveform as a sum of template pulses. This allows the algorithm to discriminate consecutive discharges "hidden" on the falling edge of primary pulses, even with small time separations ($\Delta t \approx 5$ ns).
2. Event Selection: Primary laser-induced pulses are tagged based on timestamp and amplitude. A "veto" window ensures cell recovery. Only waveforms with exactly one primary discharge are analyzed to isolate the first secondary event.
3. Parameter Extraction: The time-interval distribution ($\Delta t$) between the primary pulse and the first secondary pulse is fitted using a model that accounts for:
   • Background DCR.
   • Exponential decay of afterpulses ($e^{-\Delta t / \tau_{AP}}$).
   • Sensor recovery functions (Geiger discharge probability and charge recovery).
   • Algorithm detection efficiency (modeled via a sigmoid function).

3. Key Contributions

• Single-Cell Isolation: The use of a dedicated single-cell readout structure effectively suppresses spatial optical crosstalk, allowing for the direct measurement of intrinsic temporal afterpulsing without contamination from neighboring cells.
• Advanced Signal Processing: The development and validation of an MLR-based pulse-finding algorithm capable of resolving overlapping pulses with high precision (50% efficiency threshold at $\approx 5$ ns separation).
• Comprehensive Validation: The analysis framework was rigorously tested against a single-cell Monte Carlo simulation that included recursive afterpulsing and electronic noise, confirming the accuracy of the extraction methods.
• Radiation Damage Study: Systematic characterization of afterpulsing dynamics across a wide range of neutron fluences ($0$ to $10^{13} \text{ cm}^{-2}$) and overvoltages.

4. Key Results

The study yielded the following quantitative findings for overvoltages in the range of 3–5 V:

• Afterpulse Probability ($P_{AP}$): The total afterpulse probability was found to be below 6%.
• De-trapping Time Constant ($\tau_{AP}$): The characteristic time constant for trap release was found to be below 10 ns.
• Independence from Fluence: Crucially, neither $P_{AP}$ nor $\tau_{AP}$ showed a significant dependence on the irradiation fluence. The values remained consistent across the fresh reference and the two irradiated samples.
• Saturation: The integrated afterpulse probability saturates for time intervals $\Delta t > 30$ ns.

5. Significance and Conclusion

• Mechanism Identification: The lack of dependence on radiation fluence suggests that the observed afterpulsing in the 600 ns measurement window is not driven by radiation-induced deep traps. Instead, the mechanism is likely dominated by shallow defects or optically-induced delayed crosstalk inherent to the device structure.
• Limitations: The current 600 ns window is insufficient to detect long-term trapping effects that may occur on the microsecond scale.
• Future Work: The authors conclude that to fully understand radiation damage in SiPMs, future studies must extend the measurement window to the microsecond scale and include temperature-dependence studies to determine activation energies and definitively distinguish between lattice defects and delayed crosstalk.

In summary, this paper provides a robust framework for isolating and measuring intrinsic afterpulsing in SiPMs, demonstrating that for the specific fluences and time scales tested, radiation damage does not significantly alter the fast afterpulsing characteristics of these devices.