Using a 4-megapixel hybrid photon counting detector for fast, lab-based nanoscale x-ray tomography

This paper demonstrates that hybrid photon counting detectors (HPCDs) enable fast, lab-based nanoscale x-ray tomography, achieving an 800-fold speedup and 75–80 nm spatial resolution for imaging 130-nm node integrated circuits compared to previous methods.

The Gist

The Big Idea: A Super-Speed Camera for Tiny Chips

Imagine you are trying to take a 3D picture of a city, but the city is made of billions of tiny roads and buildings, each smaller than a single grain of sand. This is what engineers face when they try to inspect modern computer chips (Integrated Circuits).

For a long time, taking these pictures has been like trying to photograph a hummingbird with a slow, old-fashioned camera. You either get a blurry picture, or you have to wait days for the shutter to click enough times to get a clear image.

This paper is about swapping that old camera for a brand-new, super-fast, high-definition digital camera. The team at NIST (a US science lab) installed a special detector called a Hybrid Photon Counting Detector (HPCD) onto their lab equipment. The result? They can now see the inside of a computer chip in hours instead of days, with incredible clarity.

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The Problem: The "Starving" Detective

To see inside a chip without breaking it, scientists use X-rays. Think of X-rays as a flashlight beam.

• The Old Way: They used a detector that was like a small, dim flashlight with only 240 "pixels" (tiny sensors). It was so weak that it took 240 hours (10 days!) to gather enough light to build a 3D picture of a tiny section of a chip. It was like trying to fill a swimming pool with a teaspoon.
• The New Way: They installed the new HPCD. This detector is a giant wall of 4 million pixels. It's like replacing that teaspoon with a firehose. It catches light so efficiently that they gathered 40 times more data in just 10 hours.

The Result: They didn't just get a picture; they got a picture 800 times faster than their previous best attempt.

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The Challenge: The "Funhouse Mirror" Effect

Here is where it gets tricky. Because the new detector is so huge (about the size of a large pizza box) and sits close to the tiny chip, it creates a geometric distortion.

Imagine you are standing in the middle of a large room holding a flashlight. The light hits the wall right in front of you brightly. But the light hitting the corners of the room is dimmer and stretched out because of the angle.

• The Issue: If you just take a photo with this setup, the center of your image looks bright and sharp, but the edges look dim and distorted. If you tried to build a 3D model from this, the edges would look like a funhouse mirror reflection—warped and wrong.
• The Fix: The team wrote a special computer program to act like a "digital straightener." They calculated exactly how the light bends and dims across the detector and corrected the math. This ensured that the final 3D image was perfectly flat and true to life, not warped by the detector's size.

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The "Limited Angle" Puzzle

Usually, to take a 3D X-ray (like a CT scan at a hospital), you spin the object all the way around (360 degrees).

• The Constraint: In their lab, the chip is mounted on a delicate stage. If they spin it too far, it might crash into the machine. They could only rotate the chip about 45 degrees to the left and right.
• The Magic: Usually, a limited spin means a blurry 3D picture. However, because their new detector is so wide, it catches X-rays coming from many different angles at the same time.
  • Analogy: Imagine trying to guess the shape of a statue by looking at it from one spot. If you stand still, you only see the front. But if you have a giant panoramic window in front of you, you can see the front, the sides, and even a bit of the back all at once, even if you don't move your head.
  • By combining this "panoramic view" with a few small rotations, they managed to build a high-quality 3D model without needing to spin the chip all the way around.

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What Did They Actually See?

They tested this on a computer chip made with 130-nanometer technology (a very old, but still complex, chip design).

• The Features: They needed to see wires that are 160 nanometers wide. To put that in perspective, a human hair is about 80,000 nanometers wide. These wires are thinner than a strand of hair by a factor of 500.
• The Resolution: Their new system could clearly see these wires with a resolution of about 75–80 nanometers.
• The Speed: They did this in 10 hours. Their old method would have taken 240 hours.

Why Does This Matter?

Right now, if a computer chip breaks, engineers have to cut it open with a laser or a knife to see what's wrong. This destroys the chip.

• The Future: With this new tool, factories can look inside a chip, find the broken wire, and fix it without destroying the chip, and they can do it in a single workday.
• The Analogy: It's the difference between having to smash a watch to see why the gears stopped, versus using a magic X-ray glasses that let you see the gears spinning inside while the watch is still ticking.

Summary

The team took a massive, high-speed camera, figured out how to fix the weird distortions it caused, and used it to take a 3D picture of a microscopic computer chip. They did it 800 times faster than before, proving that we can now inspect the tiniest parts of our technology quickly, cheaply, and without breaking them.

Technical Summary

1. Problem Statement

Nanoscale X-ray Computed Tomography (nano-xCT) is critical for non-destructive failure analysis and metrology in the semiconductor industry, particularly for inspecting integrated circuits (ICs) with features shrinking to the nanometer scale. However, current laboratory-based nano-xCT tools face significant limitations:

• Speed vs. Resolution Trade-off: Existing lab tools typically offer spatial resolutions in the 300 nm to 1 µm range. Achieving higher resolutions (e.g., <100 nm) usually requires synchrotron sources, which are not available on-demand for industrial failure analysis.
• Photon Starvation: Lab-based systems are often "photon-starved," requiring extremely long acquisition times (hundreds of hours) to collect enough photons for high-resolution 3D reconstructions.
• Destructive Alternatives: Techniques like Focused Ion Beam Scanning Electron Microscopy (FIB-SEM) offer high resolution but are destructive, consuming the sample during measurement.
• Detector Limitations: Previous lab-based efforts using small-area detectors (e.g., 240-pixel spectrometers) lack the active area and count rate efficiency needed for rapid, high-resolution imaging of large IC regions.

2. Methodology

The authors integrated a commercial 4-megapixel Hybrid Photon Counting Detector (HPCD), specifically the DECTRIS Eiger2 R 4M, into a custom, SEM-based nano-xCT system developed at NIST.

• Experimental Setup:

  • Source: A Scanning Electron Microscope (SEM) generates X-rays by striking a Platinum (Pt) target deposited on the back of a thinned IC sample (130-nm node, Cu logic circuit).
  • Geometry: The system operates in a cone-beam configuration with a Source-Detector distance (SD) of 256 mm and a Source-Feature distance (SF) of ~10.26 µm, yielding a geometric magnification ($M_G$) of ~25,000.
  • Sample: The IC was thinned to ~3.32 µm (six circuit layers) and mounted on a rotation stage.
  • Acquisition: Data was collected at 7 discrete rotation angles (from -22.5° to +22.5°). At each angle, the beam was raster-scanned over a ~25 µm × 10 µm area.

• Technical Challenges & Corrections:

  • Geometric Corrections: Due to the large active area of the HPCD (155 mm × 162 mm) relative to the source distance, significant intensity variations occur across the detector. The authors applied corrections for:
    1. Solid Angle Variation: A $(z/r)^3$ effect where $z$ is the distance to the center pixel and $r$ is the distance to an arbitrary pixel.
    2. Pixel Obliquity: The effective area of pixels facing the source decreases at the edges.
    3. Absorption Probability: While energy-dependent absorption changes were calculated, they were deemed negligible (<1%) for the dominant 4–10 keV photon energies in this setup.
  • Limited Angle Tomography: The sample could only rotate ±45° due to SEM chamber constraints. The authors utilized the large detector's subtended angle (33.5°–35°) to achieve "single-angle" tomography capabilities, effectively increasing the angular coverage per discrete rotation step.

• Reconstruction Algorithm:

  • Data was processed using TomoScatt, a physics-based, table-driven reconstruction code.
  • The workflow involved a two-step optimization: a Maximum Likelihood (ML) extremization to generate a starting guess, followed by a Maximum A Posteriori (MAP) reconstruction with a Bayesian prior to produce a high-fidelity, low-noise 3D volume.
  • Inter-angle alignment was performed by aligning partial 3D reconstructions rather than raw 2D radiographs to minimize displacement errors.

3. Key Contributions

• Integration of HPCD in Lab Settings: Demonstrated the first successful integration of a large-area (4MP) HPCD into a tabletop SEM-based nano-xCT system, proving its viability outside of synchrotron facilities.
• Geometric Correction Framework: Developed and validated a comprehensive correction model for large flat-panel detectors in cone-beam geometry, specifically addressing the $(z/r)^3$ intensity fall-off which is critical for accurate white-field statistics in tomography.
• Quantitative Image Quality Metrics: Applied rigorous, standard metrics (Modulation Transfer Function [MTF], Fourier Shell Correlation [FSC], and Contrast-to-Noise Ratio [CNR]) to objectively quantify resolution and image quality, moving beyond qualitative visual inspection.
• Limited Angle Strategy: Showed how the large detector's field of view can compensate for limited sample rotation angles, enabling high-quality 3D reconstruction with fewer discrete rotation steps.

4. Results

• Speed and Efficiency:
  • The new setup collected data for a full 3D reconstruction of a ~1200 µm³ region in just over 10 hours.
  • This represents a 20-fold increase in speed compared to the previous system (which used a 240-pixel spectrometer and took ~240 hours).
  • The system collected 40 billion photons, a 40-fold increase in photon count compared to the previous 1 billion photons.
  • Overall Speedup: The combination of faster acquisition and higher photon collection resulted in an 800× overall speedup in effective data collection efficiency.
• Resolution and Image Quality:
  • Feature Resolution: The system clearly resolved 160 nm wiring features in the 130-nm node IC.
  • Quantitative Metrics:
    • CNR: Measured at 69 for wire features, far exceeding the Rose Criterion (CNR > 5) for distinguishability.
    • FSC: The Fourier Shell Correlation analysis yielded a resolution of 77 nm (at the 0.5 threshold), indicating the system is not limited by the instrument's inherent resolution but by the experimental parameters.
    • MTF: Confirmed high-frequency transfer capabilities consistent with the FSC results.
  • Downsampling: Analysis showed that comparable image quality could be achieved with less than 2 hours of data acquisition, suggesting further potential for speed optimization.

5. Significance

• Industrial Impact: This work bridges the gap between high-resolution synchrotron imaging and practical, in-house industrial metrology. It provides semiconductor foundries with a tool capable of non-destructive failure analysis at the 130-nm node (and potentially smaller) with turnaround times compatible with production cycles (days rather than months).
• Technological Advancement: It establishes that Hybrid Photon Counting Detectors are not just for synchrotrons but are transformative for laboratory X-ray imaging, offering high quantum efficiency (>80%), zero dark counts, and ultra-high count rates.
• Future Potential: The results suggest that with further optimization (e.g., smaller SEM focal spots), spatial resolutions below 75 nm are achievable in a lab setting. This opens the door for routine, non-destructive inspection of advanced front-end-of-line (FEOL) features in next-generation chips, a capability currently lacking in the industry.