Study of Particle Fluence Effects on Collected Charge and Depletion Voltage of the ATLAS IBL Planar Pixel Sensors

This paper analyzes the evolution of collected charge and depletion voltage in ATLAS IBL planar pixel sensors over a decade of LHC operation, correlating radiation-induced performance degradation with particle fluence using experimental bias scans and validated TCAD/Monte Carlo simulations.

The Gist

The Big Picture: A Detective Story in a Tiny World

Imagine the ATLAS detector at CERN as a giant, high-speed camera trying to take pictures of tiny particles smashing into each other. The most important part of this camera is its "innermost lens," called the Insertable B-Layer (IBL). This layer is made of thousands of tiny silicon sensors (like the chips in your phone, but much tougher) that act as the camera's retina.

For ten years, this camera has been taking pictures inside a nuclear particle accelerator. But there's a problem: the environment is incredibly hostile. It's like trying to take photos in a room where millions of tiny, invisible bullets (radiation) are flying around every second. Over a decade, these "bullets" have battered the sensors, damaging their internal structure.

This paper is a report card on how well these sensors are still working after ten years of being shot at. The scientists wanted to answer two main questions:

1. How much "signal" are the sensors still catching? (Charge Collection)
2. How much "power" do we need to turn them on to get a clear picture? (Depletion Voltage)

The Damage: The "Clogged Highway" Analogy

Think of the silicon sensor as a highway where cars (electrons) need to drive from one side to the other to deliver a message (the signal).

• Before the damage: The highway is smooth and empty. The cars drive fast and arrive quickly.
• After 10 years of radiation: The "bullets" have created potholes and roadblocks (defects) all over the highway.
  • The Traffic Jam: The cars (electrons) get stuck in these potholes. Some never make it to the end. This means the signal gets weaker. This is called a loss of Charge Collection Efficiency.
  • The Power Struggle: To get the cars moving fast enough to jump over the potholes before they get stuck, you need to push them harder. In the sensor, this "push" comes from electricity (voltage). As the damage gets worse, you have to turn up the voltage dial higher and higher just to keep the traffic moving. This is the Depletion Voltage.

What the Scientists Did

The team didn't just guess; they ran a series of tests called "Bias Voltage Scans."

Imagine you are testing a dimmer switch on a lightbulb that is getting old and damaged. You slowly turn the knob up from low to high and measure how bright the light gets.

• The Test: They took the ATLAS sensors and slowly increased the voltage (the "push") while the LHC was running.
• The Observation: They watched how much "charge" (the light brightness) the sensors collected at each voltage level.

They did this at different times over the last ten years, from when the sensors were brand new (2015) to when they were heavily damaged (2025).

The Key Findings

1. The Sensors Are Still Working (But Need a Boost)
Even after being hit by a massive amount of radiation (more than 2 quadrillion neutrons per square centimeter!), the sensors are still doing their job. However, they are "tired."

• The Result: To get the same clear picture they used to get with a low voltage, they now need a much higher voltage.
• The Analogy: It's like an old runner who used to run a mile in 10 minutes with a light jog. Now, after years of running in mud, they need to sprint at maximum speed just to finish the same mile.

2. The "Depletion Voltage" Keeps Rising
The scientists found a clear pattern: as the radiation damage increased, the voltage needed to make the sensor work perfectly went up in a straight line.

• The Numbers: In 2016, they needed about 80 Volts. By 2025, they needed 650 Volts.
• The Future: They predict that by the end of the current run in 2026, they will need about 540–580 Volts just to keep the sensors fully "depleted" (fully active). They are currently running them at 650 Volts to be safe.

3. The Deep Parts of the Sensor Are Struggling
The sensors are 200 micrometers thick (about the width of two human hairs).

• The Problem: When a particle hits the sensor, it creates charge all the way through the thickness. If the charge is created deep inside the sensor, it has a long way to travel.
• The Finding: In the heavily damaged sensors, the "roadblocks" in the deep middle of the sensor are so bad that even with high voltage, some charge gets trapped before it can escape. This means the signal from the deepest parts of the sensor is weaker than the signal from the surface.

4. Computers Got It Right
The scientists used super-computers (TCAD simulations) to model exactly what should happen based on physics laws. They compared their computer models with the real data from the detector.

• The Verdict: The computer models were incredibly accurate. They predicted exactly how the sensors would behave, how much voltage would be needed, and how the signal would drop. This proves that our understanding of how radiation damages silicon is very good.

The Conclusion

After ten years of operation, the ATLAS IBL planar sensors are like veteran soldiers who have seen a lot of battle. They are scarred and damaged, and they require a lot more energy (voltage) to function than they did when they were new.

However, they are not broken. By turning up the voltage dial to 650 Volts, the scientists can still get clear, high-quality data. The paper confirms that the sensors will continue to work effectively through the end of the current run in 2026, provided they are given enough electrical "push" to overcome the radiation damage.

In short: The sensors are tired and need a stronger push to work, but thanks to careful monitoring and high voltage, they are still taking great pictures of the universe.

Technical Summary

Technical Summary: Study of Particle Fluence Effects on Collected Charge and Depletion Voltage of the ATLAS IBL Planar Pixel Sensors

Problem Statement
After a decade of operation at the Large Hadron Collider (LHC), the planar pixel sensors comprising the innermost barrel layer (Insertable B Layer, or IBL) of the ATLAS detector have accumulated a significant particle fluence, exceeding $2 \times 10^{15}$ $1\text{ MeV-neq/cm}^2$. This radiation exposure induces bulk damage in the silicon sensors, manifesting macroscopically as increased leakage current, reduced charge collection efficiency (CCE), and a rising depletion voltage. Understanding the evolution of these parameters is critical for maintaining the spatial resolution of reconstructed pixel hits and the efficiency of identifying pixel clusters in dense hadronic jets. While previous studies have addressed these effects in microstrip and 3D pixel sensors, this work focuses specifically on the long-term evolution of the IBL planar sensors, covering a fluence range spanning two orders of magnitude.

Methodology
The study utilizes a comprehensive dataset of $pp$ collision events collected during Run 2 (2015–2018) and Run 3 (2022–2025) of the LHC. The analysis relies on dedicated bias voltage scans performed at the beginning and end of each data-taking campaign. These scans measure the most probable value (MPV) of the collected cluster charge as a function of the applied reverse-bias voltage ($V_{bias}$).

Key methodological components include:

• Data Selection: Only pixel clusters associated with reconstructed charged-particle tracks ("hits-on-track") are considered. Tracks are selected with transverse momentum ($p_T$) thresholds of 0.7 GeV for charge studies and 3 GeV for depth-dependent studies. Cluster charges are rescaled by $\cos \alpha$ to account for the particle incidence angle.
• Depletion Voltage Determination: The depletion voltage ($V_{depl}$) is defined as the transition point between the charge collection regimes proportional to $\sqrt{V}$ (undepleted) and $V$ (fully depleted or dominated by trapping effects). This is determined via an iterative $\chi^2$ fit using linear and square-root functions to the charge-vs-voltage data.
• Simulation and Modeling: The experimental data are compared against two simulation frameworks:
  1. ATLAS Radiation Damage Digitizer: A Monte Carlo (MC) simulation incorporating a radiation damage digitizer that models charge carrier drift, trapping, and signal induction using the Bichsel model and TCAD-derived electric field profiles.
  2. Standalone TCAD Simulations: Technology Computer Aided Design (TCAD) simulations using the Silvaco toolset to model the electric field profiles, carrier velocities, and trapping effects based on the Chiochia model for radiation-induced defects.
• Fluence Estimation: Particle fluence is estimated from leakage current measurements, yielding a conversion factor of $(5.40 \pm 0.35) \times 10^{12} \text{ neq cm}^{-2}/\text{fb}^{-1}$.

Key Contributions and Results

• Charge Collection Efficiency (CCE) Evolution: The study documents the CCE as a function of integrated luminosity and fluence. Data show a good agreement with simulation predictions over nearly two orders of magnitude of fluence. A slight deviation, where data exhibit moderately higher CCE than simulations at fluences above $\approx 1.5 \times 10^{15} \text{ neq/cm}^2$, is observed, potentially indicating a sub-linear dependence of charge trapping on accumulated fluence.
• Depth-Dependent Collection: The analysis confirms that charge trapping reduces CCE as the depth of charge generation increases. The simulation accurately models the fraction of collected charge as a function of depth for various fluence and bias voltage conditions.
• Depletion Voltage Scaling: The fitted depletion voltage increases linearly with integrated luminosity and fluence. The value evolved from approximately 110 V (after 42 $\text{fb}^{-1}$) to 500 V (after 410 $\text{fb}^{-1}$). The linear scaling holds for both data and simulation, allowing for predictions of the depletion voltage at the end of Run 3 (estimated at 540 $\pm$ 45 V from data and 580 $\pm$ 70 V from simulation).
• High-Fluence Behavior: At the highest fluences reached ($\approx 2.5 \times 10^{15} \text{ neq/cm}^2$), the charge collection vs. bias voltage curve becomes approximately linear across the entire scan range. The distinct transition between $\sqrt{V}$ and $V$ regimes disappears. This is interpreted via TCAD simulations as a state where electrons generated in the deeper bulk regions have collection times exceeding their trapping times for all applied bias voltages (up to 650 V). Consequently, the operational bias voltage for 2026 is set to 650 V based on hit-on-track efficiency rather than depletion voltage extraction.
• Physical Interpretation: The transition in charge collection behavior is linked to the saturation of electron drift velocities. TCAD simulations reveal that the electric field minimum in the sensor bulk rises above the critical field strength ($\approx 10^4 \text{ V/cm}$) required for velocity saturation at bias voltages around 250 V. This saturation reduces the sensitivity of collection time to further voltage increases, altering the functional dependence of the collected charge.

Significance
This paper provides the most extensive dataset available on the radiation damage effects in ATLAS IBL planar sensors, spanning ten years of LHC operation. It validates the ATLAS radiation damage simulation models across a wide range of fluences, confirming their utility for predicting sensor performance and optimizing operating conditions. The study establishes a linear relationship between depletion voltage and fluence for planar sensors in this regime, offering a robust method for monitoring sensor health. Furthermore, the identification of the linear charge-voltage regime at high fluences clarifies the physical limitations of charge collection in heavily irradiated silicon, guiding the operational strategy for the final year of Run 3. The results confirm that despite significant bulk damage, the sensors remain operational at high bias voltages, ensuring the continued performance of the ATLAS inner tracking system.