Temperature dependence of the long-term annealing behavior of neutron irradiated diodes from 8-inch p-type silicon wafers

This study investigates the isothermal annealing behavior of neutron-irradiated p-type silicon pad diodes from 8-inch wafers across a range of fluences and temperatures to extract annealing time constants, thereby improving the Hamburg model's ability to predict long-term radiation damage effects in the CMS High-Granularity Calorimeter sensors for the High-Luminosity LHC.

The Gist

The Big Picture: A Super-Strong Shield for a Super-Strong Machine

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle smasher. It's about to get a massive upgrade called the High-Luminosity LHC (HL-LHC). Think of this upgrade as turning a standard highway into a super-highway where traffic (particles) increases tenfold.

The problem? This massive traffic jam creates a lot of "radiation pollution." The detectors (the cameras taking pictures of the collisions) are made of silicon, which is like a very sensitive digital camera sensor. If you leave a camera in a radioactive environment for too long, the sensor gets "bruised" or damaged. It starts getting noisy (leaking current) and blurry (losing charge collection).

To survive this, scientists are building a new detector called HGCAL. They need to know exactly how long their silicon sensors will last and how they recover when the machine is turned off for maintenance. This paper is a "stress test" report on those sensors.

The Experiment: The "Baking and Cooling" Test

The scientists took slices of silicon (wafers) and gave them a massive dose of radiation damage, simulating years of operation in just a few minutes. Then, they put these damaged sensors into different "environments" to see how they heal.

Think of the sensors as broken glass that has been cracked by radiation. The scientists wanted to see if the glass could "heal" itself over time, and how temperature affects that healing.

They tested the sensors at five different temperatures:

1. The "Fridge" (5.5°C): Very cold, like a winter day.
2. Room Temperature (20.5°C): Standard office temp.
3. Warm (30°C - 40°C): Like a hot summer day or a warm bath.
4. The "Oven" (60°C): The standard "baking" temperature used to speed up aging tests.

The Analogy: Imagine you have a bruised apple.

• If you leave it in the fridge, the bruise heals very slowly.
• If you leave it on the counter, it heals at a normal pace.
• If you put it in a warm oven, it heals (or rots) much faster.

The scientists wanted to figure out the exact "healing recipe" so they could predict how the sensors would behave during the years the LHC is shut down for maintenance (when the sensors are cold) versus when it's running hot.

The Two Types of Silicon: "Float Zone" vs. "Epitaxial"

The study used two different types of silicon sensors, which are like two different breeds of dogs:

• Float Zone (FZ): The "standard" breed.
• Epitaxial (EPI): A thinner, more delicate breed (like a Chihuahua compared to a Labrador).

They found that these two breeds heal at different speeds. The "Chihuahua" (Epitaxial) tends to recover faster initially but behaves differently than the "Labrador" (Float Zone). This is important because the new detector uses both types in different areas.

The Three Stages of "Healing" (Annealing)

When the sensors are damaged, they go through three phases, which the scientists tracked like a doctor monitoring a patient:

1. The "Beneficial" Phase (The Good News):
   Immediately after the damage, the sensors actually get better for a short while. It's like a muscle that gets a little stronger after a workout. The sensors become more efficient at collecting signals.

   • Finding: The "Chihuahuas" (Epitaxial) reach this peak health faster than the "Labradors" (Float Zone).

2. The "Reverse" Phase (The Bad News):
   After the initial boost, the sensors start getting worse again. This is called "reverse annealing." It's like the muscle getting sore and stiff after the workout. The damage starts to accumulate again, making the sensor less efficient.

   • Finding: This is the long-term danger zone. The scientists needed to know exactly how fast this happens at different temperatures.

3. The "Charge Multiplication" Surprise:
   For the sensors that were hit with the most radiation and left in the hot oven (60°C) for a very long time, something weird happened. The sensors started creating extra charge on their own.

   • Analogy: It's like a microphone that starts picking up its own echo and amplifying it until it squeals. While this sounds cool, it actually means the sensor is getting too noisy and might break. Fortunately, this only happens after a very long time, far beyond what the detector will experience in its lifetime.

The Big Discovery: The "Hamburg Model" Needs an Update

For years, scientists have used a rulebook called the Hamburg Model to predict how silicon sensors age. It's like a weather forecast that says, "If it's 60°C, the sensor will heal in 100 minutes."

This paper found that the weather forecast is wrong.

• The Sensors are Slower: The sensors in this study healed much slower than the Hamburg Model predicted. It's like the model said the bruised apple would heal in an hour, but it actually took three.
• Temperature is Tricky: The model assumed that cooling the sensors down (during shutdowns) would stop the damage almost completely. The new data shows that even at low temperatures, the damage continues to evolve, just at a different rate than expected.
• The "Chihuahua" vs. "Labrador" Difference: The old model treated all silicon the same. This study proves that the thin, delicate sensors behave differently than the thick, standard ones.

Why Does This Matter?

The CMS detector at CERN is going to run for years in a super-radiation environment. If the scientists use the old "Hamburg Model" to plan their maintenance, they might think the sensors are healthy when they are actually failing, or vice versa.

By creating a new, more accurate recipe for how these specific sensors heal and age, the scientists can:

1. Plan better shutdowns: Know exactly how long to keep the machine off to let the sensors recover.
2. Predict the future: Know exactly when the sensors will need to be replaced.
3. Save the experiment: Ensure the HGCAL detector survives the entire HL-LHC upgrade without failing.

The Bottom Line

This paper is a "user manual update" for the silicon sensors of the future. The scientists took a bunch of broken silicon, baked them at different temperatures, and realized that the old instructions were too optimistic. The sensors are tougher but slower to heal than we thought, and they need a new, more precise guide to ensure they survive the high-energy traffic of the future.

Technical Summary

1. Problem Statement

The High-Luminosity Large Hadron Collider (HL-LHC) upgrade will increase the integrated luminosity by a factor of ten, subjecting the CMS detector's Calorimeter Endcap (CE) to extreme radiation levels. The High-Granularity Calorimeter (HGCAL) will utilize silicon pad sensors in regions with fluences ranging from $1.0 \cdot 10^{14}$ to $1.0 \cdot 10^{16} \, \text{neq/cm}^2$.

A critical challenge is predicting the long-term annealing behavior of these sensors during the HL-LHC's operational cycles, specifically during year-end technical stops and long shutdowns. The existing Hamburg model, which describes radiation damage and annealing in silicon, was primarily established using n-type sensors and lower fluence ranges. There is a need to validate and potentially refine this model for p-type silicon sensors (both Floatzone and Epitaxial) at the high fluences expected in the HGCAL, particularly to accurately estimate performance degradation during shutdown periods where temperatures differ from the standard $60^\circ\text{C}$ reference.

2. Methodology

The study employed a comprehensive experimental campaign involving 35 dedicated $5 \times 5 \, \text{mm}^2$ test diodes fabricated on 8-inch p-type wafers.

• Sample Characteristics:
  • Materials: Floatzone (FZ) sensors (200 $\mu$m and 300 $\mu$m thickness) and Epitaxial (EPI) sensors (120 $\mu$m thickness).
  • Irradiation: Samples were irradiated with reactor neutrons at the Jožef Stefan Institute (Ljubljana) to fluences between $2 \cdot 10^{15}$ and $1.5 \cdot 10^{16} \, \text{neq/cm}^2$ (including a +50% safety factor over HL-LHC expectations).
• Annealing Protocol:
  • Samples were divided into five batches and subjected to isothermal annealing at five distinct temperatures: $5.5^\circ\text{C}$, $20.5^\circ\text{C}$, $30.0^\circ\text{C}$, $40.0^\circ\text{C}$, and $60.0^\circ\text{C}$.
  • The $5.5^\circ\text{C}$ temperature approximates the planned shutdown temperature, while $60^\circ\text{C}$ is the standard reference.
• Measurement Techniques:
  • IV (Current-Voltage): Leakage current measurements to determine the current-related damage rate ($\alpha$).
  • CV (Capacitance-Voltage): Used to extract the saturation voltage (analogous to depletion voltage in irradiated sensors) to calculate the Effective Doping Concentration ($N_{eff}$).
  • TCT (Transient Current Technique): Laser-induced charge collection measurements to determine Charge Collection Efficiency (CCE).
  • Measurements were conducted at $-20^\circ\text{C}$ to minimize thermal noise and ensure consistency.
• Data Analysis:
  • Data was fitted using the Hamburg model equations to extract annealing parameters: beneficial annealing time constants ($\tau_a$), reverse annealing time constants ($\tau_\gamma$), and defect introduction rates ($g_a, g_\gamma, g_c$).
  • Scaling factors were derived to extrapolate annealing behavior from the measured temperatures to any other temperature (e.g., $0^\circ\text{C}$ or $5.5^\circ\text{C}$).

3. Key Contributions

• High-Fluence Validation: This is one of the first studies to systematically characterize p-type silicon annealing at fluences up to $1.5 \cdot 10^{16} \, \text{neq/cm}^2$, a regime where the standard Hamburg model's applicability was uncertain.
• Material Differentiation: The study explicitly separates and compares Floatzone (FZ) and Epitaxial (EPI) materials, revealing distinct annealing behaviors that were previously not fully characterized at these fluences.
• Temperature Scaling Models: New empirical equations were derived to calculate acceleration factors for annealing time constants, allowing for more accurate predictions of sensor performance during the specific temperature conditions of HL-LHC shutdowns.
• Correction of In-Reactor Annealing: The authors recalculated the equivalent annealing time accumulated during the irradiation process itself, correcting for the fact that sensors warm up during irradiation, which significantly impacts the initial state of the samples.

4. Key Results

• Deviation from Hamburg Model:
  • Slower Annealing: The extracted annealing time constants ($\tau$) for both FZ and EPI sensors were generally higher than predicted by the standard Hamburg model. This implies that annealing proceeds slower than previously assumed.
  • Shifted Minima: Consequently, the time required to reach the minimum in effective doping concentration ($N_{eff}$) is delayed. For example, at $60^\circ\text{C}$, the minimum occurs later than the standard ~80 minutes predicted by the model.
• Temperature Dependence:
  • Reverse Annealing: The activation energy for reverse annealing was found to be lower than the Hamburg model prediction. This suggests that at lower temperatures (e.g., during shutdowns), reverse annealing proceeds faster relative to the $60^\circ\text{C}$ baseline than the standard model predicts.
  • Scaling Factors: New scaling equations were established for both FZ and EPI materials to convert annealing times between different temperatures.
• Material Differences:
  • FZ vs. EPI: EPI sensors reached their performance minimum significantly earlier than FZ sensors at all temperatures.
  • Defect Introduction Rates: The stable damage introduction rate ($g_c$) was measured to be an order of magnitude lower than the Hamburg model prediction, though no strong fluence dependence was observed within the tested range.
• Charge Collection Efficiency (CCE):
  • CCE initially increases (beneficial annealing) and then decreases (reverse annealing).
  • Charge Multiplication: For sensors annealed at $60^\circ\text{C}$ for extended periods (>1000 min), a rise in CCE was observed at high bias voltages. This is attributed to charge multiplication (impact ionization) due to the formation of a double junction and high electric fields, a phenomenon not expected to occur within the operational lifetime of HGCAL.
• Leakage Current: The standard Hamburg model fit for leakage current ($\alpha$) failed to describe the data, likely due to the high fluences causing double-junction effects and the use of fixed voltage measurements rather than depletion voltage.

5. Significance

• Improved HL-LHC Simulation: The newly extracted parameters allow for a more accurate modeling of the CMS HGCAL silicon sensors. Specifically, the revised time constants and activation energies will change the predictions of sensor performance during the long shutdowns, potentially affecting the scheduling of maintenance or the expected operational lifetime.
• Model Refinement: The results highlight that the standard Hamburg model, derived from n-type sensors at lower fluences, requires modification for p-type sensors at HL-LHC fluences. The observed differences in activation energies and time constants suggest that material properties (oxygen content, handling wafers) and fluence levels play a more critical role than previously accounted for.
• Future Directions: The authors have initiated a follow-up campaign with lower fluences ($10^{13} - 10^{14} \, \text{neq/cm}^2$) to isolate material effects from high-fluence phenomena and a campaign simulating successive irradiation/annealing cycles to mimic the actual HL-LHC operating scenario.

In conclusion, this study provides essential, data-driven corrections to the annealing models used for the CMS HGCAL, ensuring that the detector's performance predictions for the HL-LHC era are robust and based on the specific characteristics of the p-type silicon sensors being deployed.