Comparison of Silvaco and Synopsys TCAD Predictions Including the Perugia Radiation Damage Model in Silicon Pixel Detectors for the HL-LHC

This paper compares Silvaco and Synopsys TCAD simulations incorporating the Perugia radiation damage model to evaluate their predictive accuracy for key performance metrics of silicon pixel detectors under the extreme radiation conditions expected at the High Luminosity LHC.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed particle racetrack. Scientists are upgrading it to the "High-Luminosity" version (HL-LHC), which means they will be smashing particles together much more frequently. The problem? This intense traffic creates a lot of "radiation dust" that damages the silicon sensors (the cameras) trying to take pictures of the collisions.

Over time, this radiation dust turns the silicon sensors into "leaky" and "stiff" devices. They start losing their ability to collect signals (like a camera losing focus) and require much higher voltage to work, which risks breaking them.

To fix this before it happens, scientists use computer simulations to predict how the sensors will behave after years of radiation. They need to know: How much voltage do we need? How much current will leak? Will the sensor still work?

The Two "Weather Forecasters"

In this paper, the researchers are testing two different computer programs (TCAD tools) that act like weather forecasters for these sensors:

1. Synopsys
2. Silvaco

Both programs use a specific set of rules called the "Perugia Radiation Damage Model." Think of this model as a detailed instruction manual that tells the computer exactly how the "radiation dust" damages the silicon, creating tiny traps and holes that mess up the electrical flow.

The goal of this paper is to see if these two different "forecasters" give the same prediction when using the same instruction manual. If they agree, it means the manual is reliable, and scientists can trust the predictions no matter which software they use.

The Experiment: A Tiny Silicon Diode

The researchers built a virtual 2D model of a tiny silicon sensor (a diode) that is 50 micrometers thick (about the width of a human hair). They simulated two scenarios:

1. Fresh Sensor: Before any radiation hits it.
2. Radiated Sensor: After being hit by a massive amount of radiation (simulating the harsh environment of the HL-LHC).

They tested these sensors at two temperatures: a cool 248 K (about -25°C) and a warm 300 K (room temperature).

The Results: Do the Forecasters Agree?

1. The Fresh Sensor (Unirradiated)
When the sensor was brand new, both computer programs agreed almost perfectly on how much electricity flowed through it and how it stored charge, up to about 500 volts.

• The Discrepancy: When they pushed the voltage very high (near 700 volts), the programs started to disagree slightly on exactly when the sensor would "break" (breakdown). The authors suggest this is likely because the two programs use slightly different digital "grids" (meshes) to draw the sensor, similar to how two different map apps might draw a road slightly differently.

2. The Radiated Sensor (The Real Test)
This is where the real magic happened. They simulated the sensor after it had been blasted with radiation.

• Leakage Current: Both programs predicted the "leakage" (unwanted electricity) almost identically.
• Depletion Voltage: Both agreed perfectly on how much voltage was needed to make the sensor work again.
• Electric Fields: They mapped out the invisible electric forces inside the silicon. In the middle of the sensor (the "bulk"), the two programs matched almost perfectly (within 1% of each other).
• The "Traps": They also looked at the tiny "traps" created by radiation that catch electrons. The two programs agreed on the behavior of these traps within a very reasonable margin (about 20%).

The Temperature Twist:
At room temperature (300 K), the programs disagreed a bit more at the highest radiation levels. However, the authors note this isn't a big worry because, in the real world, these damaged sensors are almost never operated at room temperature; they are kept very cold to survive. So, the agreement at the cold temperature (248 K) is what really matters, and there, the two programs were in perfect sync.

The Bottom Line

The paper concludes that Synopsys and Silvaco are like two different chefs following the exact same recipe (the Perugia Model) and ending up with the same delicious dish.

Even though the software tools are different, when they use the Perugia radiation damage model, they produce nearly identical predictions for how silicon sensors will survive the harsh radiation of the future HL-LHC. This gives scientists confidence that their models are solid and that they can use either tool to design the next generation of particle detectors.

Note: The authors mention they plan to look at "collected charge" in the future, but this paper focused strictly on voltage, current, and electric fields.

Technical Summary

1. Problem Statement

The High-Luminosity Large Hadron Collider (HL-LHC) will subject silicon pixel detectors to radiation fluences 5 to 10 times higher than current levels. This intense radiation causes bulk and surface damage in silicon sensors, leading to:

• Increased leakage current.
• Shifts in operational (depletion) voltage.
• Signal loss and degradation of charge collection.
• Modifications to front-end electronics behavior.

Accurate prediction of these effects is critical for estimating operational voltages and training reconstruction algorithms. While the University of Perugia Radiation Damage Model (incorporating specific bulk and surface defect physics) has been successfully implemented in Synopsys Sentaurus TCAD, there was a need to validate its portability and predictive power in Silvaco TCAD. Without cross-validation between these two major industry-standard simulation tools, the robustness of the radiation damage modeling remains unverified for broader adoption.

2. Methodology

The authors performed a comparative study of device simulations using both Synopsys and Silvaco TCAD tools.

• Device Structure: A 2D simulation of an n-on-p diode was used.
  • Thickness: 50 µm.
  • Bulk Concentration: $5 \times 10^{12} \text{ cm}^{-3}$ (Boron).
  • Pitch: 20 µm with a small collection electrode.
  • Surface: 1 µm oxide layer.
• Physics Models: Both tools utilized identical physical models to ensure a fair comparison:
  • Statistics: Fermi-Dirac.
  • Recombination: Scharfetter - Shockley Read Hall.
  • Band-to-band tunneling: Schenk.
  • Bandgap narrowing: Slotboom.
  • Impact ionization: van Overstraeten and de Man.
• Radiation Damage Implementation: The Perugia model was ported to Silvaco. This includes:
  • Bulk Model: Two acceptor defects and one donor defect with densities proportional to fluence ($\Phi$). It utilizes a fluence-dependent function for acceptor creation ($N_A$) to handle high fluences ($> 3 \times 10^{15} \text{ neq/cm}^2$).
  • Surface Model: A continuous energy distribution of defects (acceptor-like in the upper bandgap, donor-like near the valence band) and linear oxide charge increase with dose.
• Simulation Scenarios:
  • Fluences: Unirradiated, $\Phi = 1.5 \times 10^{15} \text{ neq/cm}^2$, and $\Phi = 1.0 \times 10^{16} \text{ neq/cm}^2$.
  • Temperatures: $T = 248 \text{ K}$ and $T = 300 \text{ K}$.
• Observables: Current-Voltage (IV), Capacitance-Voltage (CV), electric field profiles, and trap ionization probabilities.

3. Key Contributions

• Model Portability: Successfully ported the complex Perugia bulk and surface radiation damage models from Synopsys to Silvaco TCAD.
• Cross-Validation: Provided the first direct comparison of these two distinct TCAD engines when simulating high-radiation environments relevant to the HL-LHC.
• Defect Statistics Analysis: Analyzed not just macroscopic electrical characteristics but also microscopic trap ionization probabilities, offering deeper insight into the consistency of defect physics implementation.

4. Results

Unirradiated Device

• IV Characteristics: Excellent agreement between tools up to ~500 V. Discrepancies appeared at higher voltages (Synopsys predicted breakdown at ~700 V vs. Silvaco at ~760 V), likely due to differences in mesh generation.
• CV Characteristics: Both tools accurately predicted a depletion voltage of ~10 V and matched the "step" feature at ~55 V (attributed to depletion under the oxide).

Irradiated Device

• Leakage Current (IV):
  • At 248 K: Remarkably good agreement across all fluences. Minor deviations occurred only at very high voltages and highest fluence, attributed to mesh differences.
  • At 300 K: Agreement was qualitative only at the highest fluence. However, the authors note this is less critical as devices are rarely operated above 0°C after such high irradiation.
• Depletion Voltage (CV): At 248 K, the agreement between the two tools was "practically perfect" for both fluences.
• Electric Field Profiles:
  • In the bulk region, the electric field profiles agreed within 1% for both fluences and all bias voltages (100 V, 300 V, 500 V).
  • Slight discrepancies were observed near front and backside implants, again attributed to mesh mismatches and implant modeling differences.
• Trap Ionization Probabilities:
  • For bulk defects (acceptor traps 1 and 2), the ionization probabilities agreed within an order of magnitude, and within 20% in the bulk region.
  • This level of agreement is considered satisfactory given the percent-level agreement in electric fields.

5. Significance

• Validation of the Perugia Model: The study confirms that the University of Perugia radiation damage model is robust and platform-independent, yielding consistent results across different TCAD software environments.
• Reliability for HL-LHC: The high degree of agreement in critical observables (leakage current, depletion voltage, and electric field) provides confidence in using these simulations to predict sensor performance under HL-LHC conditions.
• Operational Guidance: The results support the use of these models to estimate safe operating voltages and to understand signal loss mechanisms, which is essential for the design and reconstruction algorithms of the upgraded ATLAS and CMS trackers.
• Future Work: The authors plan to extend this validation to collected charge simulations, which is the ultimate metric for tracking performance.

Conclusion: The paper demonstrates that Silvaco and Synopsys TCAD tools can produce mutually consistent predictions for irradiated silicon pixel detectors when using the Perugia radiation damage model, validating the model's soundness for future high-luminosity collider applications.