Charge carrier generation in RNDR-DEPFET Detectors

This paper presents the experimental characterization of a $64\times64$ RNDR-DEPFET pixel detector, highlighting its deep sub-electron noise performance, high time resolution, and suitability for the DANAE experiment's search for light dark matter via electron recoil detection.

The Gist

The Hunt for Invisible Ghosts: A Simple Guide to the DANAE Experiment

Imagine you are trying to hear a single, tiny whisper in a room filled with the hum of a refrigerator, the wind outside, and the occasional cough. That is essentially what physicists are doing when they hunt for Dark Matter.

Dark Matter is the invisible "glue" holding galaxies together. We can't see it, but we know it's there because of how stars move. The problem? It rarely interacts with normal matter. To catch a Dark Matter particle, you need a detector so sensitive it can hear the "whisper" of a single electron being nudged by a passing ghost.

This paper describes a new, super-sensitive camera called DANAE (Direct Dark Matter Search using DEPFET with Repetitive Non-Destructive Readout) designed to do exactly that.

Here is how it works, broken down into everyday concepts:

1. The Camera: A Grid of Tiny Buckets

Imagine a digital camera, but instead of taking pictures of landscapes, it takes pictures of electrons (tiny particles of electricity).

• The Sensor: The DANAE detector is a silicon chip with a grid of 64x64 tiny squares (pixels). Think of each pixel as a microscopic bucket.
• The Job: When a Dark Matter particle bumps into the silicon, it might knock an electron loose. That electron falls into the bucket. The camera's job is to count exactly how many electrons are in the bucket.

2. The Problem: The "Static" Noise

In a normal camera, if you try to count one single grain of sand, the vibration of your hand (noise) might make you think you saw two grains. In physics, this is called noise.

• Thermal Noise: Even when the camera is cold, the atoms inside it wiggle due to heat. This wiggling creates "fake" electrons that look like real signals.
• The Solution: To hear the whisper, you need to be very quiet. The experiment is cooled down to -133°C (about 140 Kelvin) to stop the atoms from wiggling so much.

3. The Magic Trick: "Repetitive Non-Destructive Readout" (RNDR)

This is the coolest part of the paper. Usually, when a camera reads a pixel, it empties the bucket to count the contents. Once it's empty, you can't check it again.

The DANAE detector uses a special trick called RNDR-DEPFET:

• The Two-Bucket System: Inside every single pixel, there are actually two tiny buckets connected by a door.
• The Shuffle:
  1. Electrons fall into Bucket A.
  2. The camera measures Bucket A without emptying it.
  3. The door opens, and the electrons slide into Bucket B.
  4. The camera measures Bucket B.
  5. The electrons slide back to Bucket A.
• The Result: The camera can measure the same electrons hundreds of times (800 times in this experiment!) before finally clearing them out.
• Why do this? Imagine trying to weigh a feather on a shaky scale. If you weigh it once, the scale might be off. But if you weigh it 800 times and take the average, the shaking cancels out, and you get the perfect weight. This allows the detector to distinguish between 1 electron and 2 electrons with incredible precision.

4. The Data: Sorting the Good from the Bad

The researchers ran the detector for different amounts of time (from a few seconds to a few minutes) to see how many "fake" electrons appeared naturally.

• The "Bulk" vs. The "Surface":
  • The Bulk (The Middle): Electrons generated here happen randomly over time, like raindrops hitting a roof. The longer you wait, the more rain you get. This is the signal they want to understand.
  • The Surface (The Edges): Electrons generated here happen instantly when the camera starts reading, like static electricity when you rub a balloon. This doesn't depend on how long you wait.
• The Findings:
  • They found that the "rain" (thermal noise) is very low: about 18 electrons per pixel per day. This is a great result, comparable to other top-tier experiments.
  • However, they found a lot of "static" (surface noise). Every time they took a picture, about 74 fake electrons appeared instantly, regardless of how long they waited. This is higher than they hoped for, and they are working on fixing it.

5. Why This Matters

The DANAE experiment is a prototype. It's like a test drive for a new car before it goes to the race track.

• The Goal: To find Light Dark Matter. Most experiments look for heavy Dark Matter, but if Dark Matter is very light, it only gives a tiny "nudge" to an electron. DANAE is the first detector sensitive enough to catch these tiny nudges.
• The Future: The team plans to build better versions of this camera, fix the "static" noise issue, and eventually move the experiment deep underground (like in a mine) to shield it from cosmic rays, just to be sure.

The Bottom Line

This paper is about building a super-sensitive electron counter that can listen to the universe's quietest whispers. By using a clever "shuffling" technique to average out the noise, they proved they can detect single electrons. While they still have some "static" to fix, they are one step closer to solving the mystery of what Dark Matter is made of.

Technical Summary

1. Problem Statement

The direct detection of light dark matter (DM) requires sensors capable of resolving single-electron recoils with extreme precision. Traditional DM experiments often struggle with background noise, particularly thermally generated electrons (dark current) and readout noise, which can obscure rare low-energy signals.

• Challenge: To detect light DM, experiments must distinguish signals of one or two electrons from background noise. This requires sub-electron noise levels and high time resolution to analyze the Poisson statistics of thermal generation.
• Context: The DANAE (Direct Dark Matter Search using DEPFET with Repetitive Non-Destructive Readout Application Experiment) aims to address this using silicon sensors. However, characterizing the charge carrier generation rate (both bulk thermal noise and surface/readout-induced noise) in these specific detectors is critical for establishing sensitivity limits.

2. Methodology

The study focuses on the experimental characterization of a 64×64 pixel prototype detector utilizing RNDR-DEPFET (Repetitive Non-Destructive Readout Depleted p-channel Field-Effect Transistor) technology.

• Detector Architecture:
  • RNDR-DEPFET Principle: Each pixel contains two sub-pixels connected by a transfer gate. Electrons collected in the "internal gate" of one sub-pixel are shuttled back and forth between the two sub-pixels.
  • Readout Mechanism: This allows for Correlated Double Sampling (CDS) to be performed multiple times (averaging) on the same charge packet before it is cleared. This averaging reduces readout noise by a factor of $1/\sqrt{N}$, where $N$ is the number of repetitions.
  • Specifications: 450 µm thickness, 50 µm pixel pitch, total target mass of 10.7 mg.
• Experimental Setup:
  • Environment: Operated at ~140 K in a vacuum (~5 × 10⁻⁶ mbar) with aluminum heat shielding.
  • Data Acquisition: The detector operates in a rolling-shutter mode. A standard frame consists of 800 repetitions per pixel, resulting in a frame time of ~1.22 seconds.
  • Exposure Sweep: To measure generation rates, additional exposure times (100 ms to 4.0 s) were added after the standard readout sequence.
• Data Processing & Filtering:
  • Software: Custom Python-based APANTIAS (v2.0.3) software.
  • Filtering Criteria:
    • Threshold: 5-sigma cut on non-calibrated pixel spectra.
    • Pixel Masking: Border pixels, "bad" rows/columns (identified via Gaussian width anomalies, e.g., Column 34), and "hot/cold" pixels (outliers in hit distribution) were discarded.
    • Frame Rejection: Frames with average event counts >5 sigma from the median (typically occurring during initial detector settling) were removed.
    • Clustering: Adjacent pixel hits were clustered to treat multi-pixel events as single events, minimizing the impact of pile-up.

3. Key Contributions

• Characterization of RNDR-DEPFET Noise: The paper provides the first detailed experimental breakdown of charge carrier generation in a 64×64 RNDR-DEPFET array, separating time-dependent bulk generation from time-independent surface/readout generation.
• Validation of Sub-Electron Resolution: Demonstrates that with 800 repetitions, the system achieves sufficient spectral resolution to clearly distinguish single-electron peaks from the baseline noise.
• Quantification of Noise Components: The study successfully isolates two distinct noise sources:
  1. Bulk Thermal Noise: Proportional to exposure time (Poissonian).
  2. Surface/Readout Noise: Independent of exposure time (likely caused by charge transfer inefficiencies or surface states).

4. Results

• Spectral Resolution: The raw data spectrum clearly resolves the single-electron peak. Filtering defective pixels improved the peak-to-valley ratio significantly.
• Generation Rates:
  • Time-Dependent Rate ($R_{Gen}$): Determined via linear fit slope to be 0.79 ± 0.44 e⁻/s.
    • Converted to specific units: 18 e⁻/pixel/day or 7.0 e⁻/µg/day.
    • This value is comparable to the SENSEI Skipper-CCD experiment (10.8 e⁻/µg/day), validating the bulk performance of the RNDR-DEPFET technology.
  • Time-Independent Offset ($R_{Off}$): Determined via linear fit intercept to be 74.3 ± 1.2 e⁻/frame.
    • Converted: 7.7 e⁻/µg/frame.
    • Significance: This offset is significantly higher than expected and dominates the noise budget for short exposure times. It is attributed to the readout process itself (charge transfer) rather than thermal bulk generation.
• Data Yield: After applying all cuts (removing borders, bad columns, and hot/cold pixels), 3,690 pixels (out of 4,096) were analyzed, representing an effective active mass of 9.6 mg.

5. Significance and Outlook

• Dark Matter Sensitivity: The results confirm that RNDR-DEPFETs are viable for light dark matter searches, offering high time resolution and the ability to resolve single-electron events. The bulk generation rate is competitive with state-of-the-art Skipper-CCDs.
• Critical Bottleneck: The high time-independent offset (74 e⁻/frame) is the primary limitation for detecting very rare, low-energy events in short exposure windows. This noise floor must be reduced to fully exploit the detector's potential.
• Future Work:
  • Hardware Improvements: Characterization of new detectors from a recent Max Planck Society production run.
  • Operational Optimization: Implementation of a dedicated sequence to clear internal gates before repetitive readout begins to mitigate the offset.
  • Temperature Studies: Conducting exposure sweeps at various temperatures to determine the ideal operating point and the temperature dependence of the offset.
  • Calibration: Integration of a light-emitting diode (LED) for in-situ calibration in upcoming runs.

In summary, the paper establishes the baseline performance of the DANAE detector, proving its capability for sub-electron noise detection while identifying a specific, non-thermal noise source that requires engineering solutions to fully realize the experiment's sensitivity goals.