Application of exhaustive simulation flow for advanced performance prediction of monolithic active pixel sensors

This paper presents an exhaustive simulation flow that integrates TCAD, Allpix Squared, and SPICE to accurately predict the performance of monolithic active pixel sensors (MAPS), including leakage currents and irradiation effects, and validates this methodology against measurements from the Belle II TJ-Monopix2 sensor.

The Gist

Imagine you are trying to build the ultimate high-speed camera for a particle accelerator. This camera, called a Monolithic Active Pixel Sensor (MAPS), needs to take pictures of subatomic particles moving so fast that they blur everything else. To make sure this camera works perfectly, scientists need a "digital twin"—a super-accurate computer simulation that predicts exactly how the camera will behave before they even build it.

This paper describes a new, ultra-detailed way of building that digital twin. The authors call it an "exhaustive simulation flow." Think of it as upgrading from a simple sketch of a car to a full-scale, wind-tunnel-tested, engine-running virtual prototype.

Here is how they did it, broken down into simple steps:

1. Building the Blueprint (The 3D Model)

The Problem: Previous simulations were like looking at a flat map of a city. They missed the height of the buildings and the specific layout of the streets. In these sensors, the physical shape of the tiny "pixels" (the camera's individual light sensors) matters a lot. If the shape is slightly off, the electric signals get confused.
The Solution: The team took the actual blueprints (the "layout") of the sensor and built a precise 3D model of it. They included specific features, like a "deep p-well" (a special layer of material), which acts like a traffic director for electrons.
The Result: By including these 3D details, they could see exactly how electric fields flow, just like seeing how wind flows around a building. This helped them predict how much "charge" (the signal from a particle) the sensor would actually catch.

2. Simulating the "Aging" Process (Irradiation)

The Problem: These cameras are used in high-radiation environments (like the Belle II experiment in Japan). Over time, radiation damages the sensor, kind of like how sandblasting wears down a statue. This damage creates "leakage" (electrons escaping where they shouldn't) and changes how the sensor handles electricity.
The Solution: The team created a simulation that mimics this damage. They didn't just guess; they used a mathematical model (the "Perugia model") to predict how the sensor's internal currents would change as it got "worn out" by radiation.
The Result: They successfully predicted that as the sensor gets more radiation, it starts leaking more current. This is crucial because too much leakage can short-circuit the sensor's ability to read signals.

3. Testing the "Brain" of the Camera (Front-End Electronics)

The Problem: The sensor doesn't just catch particles; it has a tiny electronic brain (the front-end) that processes the signal. When radiation damages the sensor, it creates a "noise" current that confuses this brain, making it react slower or weaker.
The Solution: They connected their physics simulation (how particles move) with a circuit simulation (how the brain thinks). They used a tool called SPICE (a standard for testing electronic circuits) to see how the "brain" reacts when the sensor is damaged.
The Result: They found that the radiation causes the sensor to "discharge" too quickly, making the signal shorter and weaker. Their simulation matched real-world measurements almost perfectly, proving they understood how the damage affects the electronics.

4. The Grand Finale: The "Allpix Squared" Connection

The Big Leap: Usually, scientists use one tool to simulate physics (how particles move) and a different tool to simulate electronics (how circuits work). It's like using a weather app to design a car engine—two different languages.
The Innovation: The authors built a bridge between these two worlds. They combined Allpix Squared (the physics simulator) with SPICE (the circuit simulator) into one single flow.
The Test: They ran a simulation using a radioactive source (Iron-55) that they had also tested in the real lab.

• Before Radiation: The simulation predicted the signal strength and timing exactly as the real camera did.
• After Radiation: Even after "damaging" the virtual sensor, the simulation still matched the real, damaged camera's behavior.

Why This Matters (According to the Paper)

The paper doesn't claim this will cure diseases or build new phones. Instead, it claims this method is a game-changer for designing future particle detectors.

By using this "exhaustive" flow, scientists can now:

1. Predict performance with nanosecond precision (billionths of a second).
2. Test designs virtually before spending money to manufacture them.
3. Understand exactly how radiation will break their sensors, allowing them to design better, more resilient cameras for the next generation of particle physics experiments.

In short, they built a "crystal ball" that lets them see exactly how their particle cameras will behave in the harsh, radioactive environment of a particle collider, ensuring the next generation of experiments will be sharper and more accurate.

Technical Summary

Technical Summary: Application of Exhaustive Simulation Flow for Advanced Performance Prediction of Monolithic Active Pixel Sensors

Problem Statement
Recent advancements in Monolithic Active Pixel Sensors (MAPS), particularly regarding timing precision at the nanosecond level, have outpaced the capabilities of traditional simulation tools. Existing methodologies often fail to simultaneously address the complex physics of charge transport and the precise electrical behavior of front-end electronics, especially under irradiation conditions. The authors identify a critical need for an upgraded simulation framework that can accurately model the entire signal chain—from charge generation in the sensitive volume to the digital output of pixel logic (Time-of-Arrival and Time-over-Threshold, or ToA/ToT). This is essential for the development of next-generation sensors, such as the OBELIX sensor for the Belle II vertex detector upgrade, which must operate at room temperature after high fluence irradiation ($5 \times 10^{14} \text{ 1 MeV neq/cm}^2$).

Methodology
The paper proposes an "exhaustive simulation flow" that integrates multiple simulation domains into a unified framework, primarily leveraging the Allpix Squared Monte Carlo environment coupled with SPICE electrical simulations. The methodology is structured into four key stages:

1. 3D TCAD Layout Integration: The authors integrate the physical pixel layout (specifically the n-wells and p-wells) directly into the 3D TCAD (Technology Computer-Aided Design) model. This includes extracting layers from GDS files to model specific features like the Reduced Deep P-Well (RDPW) asymmetry found in the TJ-Monopix2 prototype. This allows for a precise description of electric fields and charge collection efficiency, accounting for charge loss in n-wells.
2. Irradiation Modeling (Physics & Electrical):
   • Charge Transport: Irradiation effects on charge propagation, such as charge trapping, are modeled.
   • Current Evolution: The evolution of leakage current ($I_{leak}$) and punch-through current ($I_{pt}$) with irradiation is simulated using the Perugia model. This involves characterizing the temperature dependence of leakage and the voltage dependence of punch-through currents between the substrate and p-wells.
   • Front-End Degradation: The impact of irradiation on the analogue front-end is modeled by introducing a current source representing the increased leakage current. This simulates the sensor discharge effect, which shortens current pulses and reduces signal amplitude. The model also accounts for transistor mismatch using foundry-provided Monte Carlo dispersion values.
3. Coupled Monte Carlo and SPICE Simulation: The core innovation is the coupling of Allpix Squared (for charge deposition, propagation, and collection) with SPICE (for front-end circuit response). This is achieved via the NetlistWriter module within Allpix Squared. Each pixel is assigned a specific mismatch ID to ensure consistent pixel-to-pixel dispersion across events while maintaining statistical variation.
4. Validation: The flow is validated against measurements from TJ-Monopix2 prototypes (samples W8R4, W2R17, W8R6) irradiated to fluences up to $5 \times 10^{14} \text{ 1 MeV neq/cm}^2$. Comparisons include I-V curves, ToT vs. injected charge curves, and $^{55}\text{Fe}$ spectral responses before and after irradiation.

Key Contributions

• Layout-Aware TCAD Modeling: The integration of specific layout features (like RDPW) into 3D TCAD models significantly improves the accuracy of charge collection efficiency predictions, showing a ~16% improvement in collected charge for RDPW compared to Full Deep P-Well (FDPW) configurations.
• Hybrid Simulation Framework: The successful coupling of Allpix Squared and SPICE allows for the simulation of realistic signal events where the electrical response of the front-end is dynamically affected by the physics of charge collection and irradiation-induced leakage.
• Comprehensive Irradiation Modeling: The approach models irradiation effects from two perspectives: charge trapping (reducing collected charge) and front-end discharge (reducing signal amplitude due to high leakage currents).
• Quantitative Validation: The methodology demonstrates the ability to reproduce complex experimental behaviors, including the shift in Time-over-Threshold (ToT) values and the degradation of signal amplitude post-irradiation.

Results

• I-V Characteristics: The Perugia model successfully reproduces the temperature dependence of leakage current ($I_{leak}$) and the general trend of punch-through current ($I_{pt}$) reduction with irradiation. While there are minor discrepancies in $I_{pt}$ simulation at high bias voltages, the model captures the operational shift allowing for lower substrate voltages post-irradiation.
• Front-End Response: The coupled simulation accurately reproduces the ToT vs. injected charge curves. Before irradiation, the simulation matches measurements within ~20% (e.g., 45 vs. 37 ToT units at 140 DAC). After irradiation, the model correctly captures the signal loss, predicting a ToT of 10 compared to a measured 8 at 140 DAC.
• $^{55}\text{Fe}$ Spectra: The simulation successfully reproduces the $^{55}\text{Fe}$ K$\alpha$ peak (approx. 1600 $e^-$) before irradiation. Post-irradiation, the simulation correctly reflects the peak broadening and reduction due to charge trapping and sensor discharge.
• Calibration Consistency: By analyzing the simulated ToT vs. collected charge, the authors derived an injection capacitance of $8.9 \text{ e}^-/\text{DAC}$, which aligns closely with the measured value of $9 \text{ e}^-/\text{DAC}$.

Significance
The paper claims that this exhaustive simulation flow provides a robust tool for the development of modern MAPS. By bridging the gap between detailed TCAD physics modeling and high-precision SPICE circuit simulation, the methodology enables accurate performance prediction for sensors operating under extreme conditions (high radiation, room temperature). The authors state that this approach is particularly valuable for the ongoing R&D of the OBELIX sensor for the Belle II experiment and is intended to be applied to future generations of MAPS. The work validates that the complex interplay between radiation damage, charge transport, and front-end electronics can be effectively modeled, reducing the reliance on trial-and-error fabrication cycles.