Timing resolution from beam tests on thin LGADs down to 16.6 ps

This paper reports that beam tests on thin, carbon-co-implanted Low-Gain Avalanche Diodes (LGADs) at DESY achieved a single-sensor timing resolution of 16.6 ps for 20 µm-thick devices and maintained a 20 ps resolution even after irradiation to high neutron fluences at cryogenic temperatures.

The Gist

Imagine you are trying to catch a speeding bullet with a camera. To get a perfect photo, your camera needs two things: it must be incredibly fast (to freeze the motion) and it must be able to see clearly even in a chaotic, crowded room.

This paper is about building the ultimate "camera" for subatomic particles. Specifically, it's about a special type of silicon sensor called an LGAD (Low-Gain Avalanche Diode). These sensors are designed to act as the "eyes" of future particle colliders, where particles smash together so violently that the environment becomes a radioactive, high-speed blur.

Here is the story of their experiment, explained simply:

1. The Problem: The "Radioactive Fog"

Future particle accelerators (like the ones at CERN) are going to be incredibly intense. Imagine a highway where the cars are moving at light speed, but there are so many of them that they crash into each other constantly.

• The Challenge: In this chaos, the sensors get hit by so much radiation that they start to "blind" themselves. The radiation damages the silicon, turning off the sensors' ability to amplify signals.
• The Goal: Scientists need sensors that are not only fast enough to time these collisions perfectly (down to the picosecond, which is a trillionth of a second) but also tough enough to survive the radiation fog.

2. The Solution: Making Sensors "Thinner"

The researchers from Italy and Germany decided to try a clever trick: make the sensors incredibly thin.

Think of a standard sensor like a thick, heavy wool blanket. When a particle hits it, it has to travel through a lot of wool, creating a messy, wobbly signal.

• The New Idea: What if we replaced the wool blanket with a single sheet of tissue paper?
• The Result: When a particle hits a thin sheet, it zips through almost instantly. The signal is sharp, clean, and fast. The less material the particle has to travel through, the less "jitter" (noise) there is in the timing.

They tested sensors ranging from 45 microns (about the width of a human hair) down to 20 microns (half the width of a hair).

3. The Experiment: The "Stopwatch" Race

To test these sensors, they set up a race track at the DESY facility in Germany using a beam of electrons (tiny particles) moving at 4 GeV/c.

• The Setup: They had a "Start Gun" (a reference sensor) and a "Finish Line" (the new thin sensors). They also had a super-accurate stopwatch (a special tube called an MCP) to check the time.
• The Test: They fired particles at the sensors and measured exactly how long it took for the signal to arrive.
• The "Irradiated" Test: To simulate the harsh environment of a future collider, they took some of the sensors and bombarded them with neutrons (like a hailstorm of tiny bullets) to see if they would still work after getting "beaten up." They then cooled these damaged sensors down to -42°C (using dry ice) to help them recover.

4. The Results: Breaking the Speed Record

The results were spectacular:

• The Speed: The thinnest sensors (20 microns) were incredibly fast. They achieved a timing resolution of 16.6 picoseconds.
  • Analogy: If a picosecond were a second, a human lifetime would be a fraction of a blink of an eye. These sensors can distinguish events that happen in that tiny fraction of time.
• The Teamwork: When they stacked two of these thin sensors together, they acted like a stereo system, improving the timing even further to 12.2 picoseconds.
• The Toughness: Even after being blasted with radiation (simulating years of use in a collider), the sensors still managed to keep a timing resolution of about 20 picoseconds. They didn't break; they just needed a little extra voltage and a cold temperature to keep working.

5. Why This Matters

Think of the Large Hadron Collider (LHC) as a giant, high-speed camera taking pictures of the universe's smallest building blocks.

• Old Sensors: Like a camera with a slow shutter speed. If two particles pass by at the same time, the photo comes out blurry. You can't tell which particle is which.
• These New Sensors: Like a camera with a super-fast shutter. They can freeze the action so clearly that scientists can separate particles that pass each other in the blink of an eye.

The Big Takeaway

By making the sensors thinner and reinforcing them with carbon (to stop radiation damage), the team proved that we can build detectors that are both super-fast and radiation-hard.

This is a huge step forward for the future of physics. It means that in the next generation of particle colliders, we will be able to see the universe with a clarity we've never had before, potentially uncovering new secrets about how the universe works, all thanks to a piece of silicon thinner than a human hair.

Technical Summary

1. Problem Statement and Motivation

Future High-Energy Physics (HEP) experiments, such as the High-Luminosity Large Hadron Collider (HL-LHC) and the Future Circular Collider (FCC-hh), will operate under extreme radiation fluence conditions (up to $\sim 6 \times 10^{16} \, \text{neq cm}^{-2}$). Existing detectors struggle to maintain both high timing resolution and radiation hardness under these conditions.

• The Challenge: Standard Low-Gain Avalanche Diodes (LGADs) typically achieve 25–35 ps timing resolution but suffer from "acceptor deactivation" (loss of gain) when exposed to high neutron fluences.
• The Proposed Solution: Reducing the substrate thickness of LGADs. Thinner sensors produce faster signals with steeper rising edges, which theoretically improves timing resolution and reduces the impact of non-uniform ionization. However, it was unclear how thin substrates (down to 15–20 µm) would perform regarding gain stability and timing precision, especially after irradiation.

2. Methodology

Device Design (EXFLU Sensors)

The study utilized two batches of sensors manufactured by Fondazione Bruno Kessler (FBK):

• EXFLU0: Based on the UFSD3.2 design but with thinner substrates (25 and 35 µm).
• EXFLU1: A dedicated design with optimized peripheral structures and substrates down to 15 µm (tested at 20, 30, and 45 µm).
• Technology: n-in-p silicon with a p+ boron gain layer ($\sim 10^{16} \, \text{cm}^{-3}$) at a depth of $\sim 1 \, \mu\text{m}$.
• Radiation Hardening: A carbon co-implant was used to mitigate boron acceptor deactivation. Two diffusion modes were tested: Low-Carbon/Low-Boron (CBL) and High-Carbon/Low-Boron (CHBL).
• Geometry: Sensors featured Single-Pad (SP) and Dual-Pad (LP) geometries. Active areas ranged from $0.75 \times 0.75 \, \text{mm}^2$ to $1.28 \times 1.28 \, \text{mm}^2$.

Experimental Setup

Tests were conducted at the DESY Test Beam Facility using a 4 GeV/c electron beam.

• Non-Irradiated Setup: Operated at ambient temperature ($18^\circ\text{C}$). The setup included a 45 µm trigger sensor, two Device-Under-Test (DUT) planes, and a Photonis Micro-Channel Plate (MCP) photomultiplier tube as a high-precision time reference.
• Irradiated Setup: Sensors irradiated with neutrons at fluences of $0.4$ to $2.5 \times 10^{15} \, \text{neq cm}^{-2}$ were tested in a cold box cooled by solidified CO$_2$ to $-42^\circ\text{C}$ to mitigate leakage current.
• Readout: Santa Cruz (SC) boards with SiGe RF transistors and Cividec amplifiers, read by a LeCroy oscilloscope (10 GSa/s, 2 GHz bandwidth).
• Analysis: Timing resolution ($\sigma_t$) was calculated using a Constant Fraction Discriminator (CFD) algorithm (30% threshold). The total resolution was decomposed into jitter ($\sigma_{jitter}$) and ionization ($\sigma_{ionisation}$) contributions.

3. Key Contributions

1. Extreme Thinness Validation: Successfully demonstrated that LGADs with active thicknesses as low as 20 µm can operate with high gain (7–40) and superior timing resolution, challenging the previous lower limits of sensor thickness.
2. Decomposition of Timing Errors: Provided a rigorous separation of timing resolution components, showing that thinner sensors significantly reduce the $\sigma_{ionisation}$ term (fluctuations in charge deposition) due to faster signal rise times.
3. Radiation Hardness at Extreme Fluence: Validated that EXFLU1 sensors (specifically the 30 µm variant) maintain gain and timing performance up to fluences of $2.5 \times 10^{15} \, \text{neq cm}^{-2}$ when operated at low temperatures, proving the efficacy of the carbon co-implant strategy.
4. Charge Efficiency: Established that thinner sensors require significantly less collected charge to achieve a specific timing precision, a critical factor for power consumption and readout bandwidth in future detectors.

4. Key Results

Non-Irradiated Performance

• Timing Resolution:
  • 45 µm: 26.4 ps
  • 35 µm: 23.4 ps
  • 30 µm: 22.0 ps
  • 20 µm: 16.6 ps (Best single-sensor result).
• Multi-Plane Tracking: A two-plane tracker system using two 20 µm sensors achieved a combined timing resolution of 12.2 ps, demonstrating the $\frac{1}{\sqrt{N}}$ scaling law.
• Gain: Measured between 7 and 40 across all non-irradiated sensors.
• Rise Time: Linearly decreased from 600 ps to 300 ps as thickness decreased from 45 µm to 20 µm.
• Charge Requirement: To achieve sub-30 ps resolution, the 20 µm sensor required only $\sim 2 \, \text{fC}$ of charge, compared to $\sim 6 \, \text{fC}$ for the 35 µm sensor (a reduction factor of >2.5).

Irradiated Performance (30 µm Sensors)

• Fluence Levels: Tested up to $2.5 \times 10^{15} \, \text{neq cm}^{-2}$.
• Timing Resolution:
  • Up to $1.5 \times 10^{15} \, \text{neq cm}^{-2}$: 18.3 ps.
  • At $2.5 \times 10^{15} \, \text{neq cm}^{-2}$: 20.5 ps (approaching the Single-Event Burnout limit).
• Gain Stability: Despite irradiation, the sensors maintained a gain between 7 and 30 when operated at high bias and low temperature ($-42^\circ\text{C}$).
• Breakdown Voltage: The breakdown voltage increased with fluence due to acceptor removal, allowing operation at higher biases (up to 400 V) to recover gain.

5. Significance and Conclusion

This paper provides critical experimental evidence that sub-20 µm LGADs are a viable and superior technology for the next generation of HEP detectors.

• Performance Leap: Achieving 16.6 ps (single sensor) and 12.2 ps (two-plane) timing resolution sets a new benchmark, surpassing the typical 25–35 ps limit of current LGADs.
• Radiation Tolerance: The study confirms that thin LGADs with carbon co-implants can survive extreme fluences while maintaining the gain necessary for precision timing, provided they are operated at reduced temperatures.
• System Efficiency: The finding that thinner sensors require significantly less charge for the same timing precision implies that future detector systems can be designed with lower power consumption and reduced data bandwidth requirements.

These results strongly support the adoption of ultra-thin, radiation-hardened LGADs for the inner tracking layers of future colliders like the HL-LHC and FCC-hh, where both extreme radiation hardness and picosecond timing are mandatory.