🔬 mesoscale physics

Determining Electron Beam Lateral Coherence in a Scanning Electron Microscope Using Electron Diffraction

This paper demonstrates the development of scanning transmission electron microscopy capabilities within a 30 keV scanning electron microscope to characterize the electron beam's lateral coherence, revealing a value exceeding 60% that is sufficient for quantum-coherent electron-light-matter interaction experiments.

Original authors: Evelijn Akerboom, Fatemeh Kiani, Giulia Tagliabue, Wiebke Albrecht, Joanne Etheridge, F. Javier García de Abajo, Albert Polman

Published 2026-06-29

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CC BY 4.0

Original authors: Evelijn Akerboom, Fatemeh Kiani, Giulia Tagliabue, Wiebke Albrecht, Joanne Etheridge, F. Javier García de Abajo, Albert Polman

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a very powerful flashlight, but instead of light, it shoots a beam of tiny electrons. Scientists usually use these "electron flashlights" in two different types of microscopes: the Transmission Electron Microscope (TEM), which is like a high-powered projector that shoots electrons through a thin slice of a sample, and the Scanning Electron Microscope (SEM), which is more like a lighthouse that scans electrons over the surface of a sample to create a 3D-like image.

This paper is about a team of scientists who wanted to make the SEM (the lighthouse) do something it usually can't do: measure how "organized" or "coherent" the electron beam is.

The Problem: Is the Beam "In Sync"?

Think of an electron beam like a marching band.

Temporal Coherence is about whether everyone is marching at the exact same speed.
Lateral Coherence is about whether everyone is marching in perfect step side-to-side.

If the band is out of step (low coherence), they can't perform complex synchronized tricks. The scientists wanted to know: If we use this SEM electron beam to try and do fancy quantum tricks (like interacting with light in a very precise way), is the beam marching in step enough to make it work?

Until now, it was hard to check this "marching order" inside an SEM because the tools to do so usually only exist in the more expensive TEMs.

The Solution: A New Trick with Twisted Graphene

The team developed a new way to test the beam's "marching order" using a technique called 4D-STEM. Imagine taking a photo of the electron beam's shadow for every single spot the beam touches, creating a massive 4D map of information.

To test the beam, they used a special material: Graphene (a sheet of carbon atoms so thin it's almost 2D). Specifically, they used a "twisted bilayer" of graphene.

The Analogy: Imagine taking two sheets of transparent paper with a honeycomb pattern drawn on them. If you stack them perfectly on top of each other, the patterns match. But if you twist one slightly, the patterns overlap to create a new, larger pattern called a Moiré pattern (like the wavy lines you see when looking through two window screens at an angle).

When the electron beam hits this twisted stack, it acts like a wave. Because the two layers of graphene are slightly twisted, the electrons bounce off them at slightly different angles. If the electron beam is perfectly "in step" (coherent), these bouncing waves will crash into each other and create a visible interference pattern (like ripples in a pond meeting and creating a new wave shape).

What They Found

The Setup Works: First, they proved they could use their SEM to see the crystal structure of gold flakes and graphene, just like a TEM can. They saw the expected hexagonal patterns, confirming their "electron lighthouse" was working correctly.
The Coherence Test: They shined the beam on the twisted graphene.
- The Calculation: They simulated what the pattern should look like if the beam were 100% perfect (100% in step).
- The Reality: They took a picture of the actual pattern. It showed the interference ripples, but they weren't as sharp as the perfect simulation.
The Result: By measuring how clear those ripples were, they calculated the beam's "marching order."
- They found that for a specific part of the beam (about 5% of its total width), the electrons were 60% in step.
- For a slightly different part of the beam, they were 20% in step.

Why This Matters (According to the Paper)

The paper concludes that this 60% level of "in-step-ness" is good enough. It proves that the SEM beam is coherent enough to attempt the fancy "quantum-coherent electron-light-matter interaction experiments" that scientists are interested in.

In simple terms: They built a new tool to check the quality of the electron beam in a standard microscope, used a twisted carbon sheet as a test ruler, and confirmed that the beam is organized enough to try some very advanced physics experiments in the future. They didn't do those advanced experiments yet; they just proved the beam is ready for them.

Technical Summary: Determining Electron Beam Lateral Coherence in a Scanning Electron Microscope Using Electron Diffraction

Problem Statement
The ability to perform quantum-coherent electron-light-matter interaction experiments in Scanning Electron Microscopes (SEMs) has gained significant interest due to the stronger interaction regimes accessible at lower electron energies (1–30 keV) compared to Transmission Electron Microscopes (TEMs). However, a critical prerequisite for these experiments is a detailed understanding of the electron beam's (e-beam) coherence properties at the specimen plane. While temporal coherence is well-understood, quantitative knowledge of lateral coherence in SEMs remains elusive. Existing methods for measuring lateral coherence, such as direct source imaging or holographic techniques, often require specialized electron-optical elements (e.g., biprisms) or long camera lengths not available in conventional SEMs. Consequently, there is a lack of established experimental methods to quantify the lateral coherence of low-energy e-beams in SEMs.

Methodology
The authors developed a 4D-Scanning Transmission Electron Microscopy (4D-STEM) capability within a standard FEI Quanta 650 SEM equipped with a thermally assisted Field Emission Gun (FEG) and a single-electron counting detector (MiniPIX TPX3). The methodology involved three progressive stages:

System Validation via SAED: The team first validated the 4D-STEM setup by performing Selected-Area Electron Diffraction (SAED) on single-crystalline gold (Au) flakes deposited on thin Si3N4 membranes. This confirmed the system's ability to collect high-quality diffraction patterns and map crystal orientations at 30 keV.
CBED Geometry Characterization: Using a monolayer of graphene, the researchers demonstrated Convergent-Beam Electron Diffraction (CBED). By adjusting the working distance (WD) and objective lens current, they achieved a semi-convergence angle of ~7.5 mrad, transitioning the diffraction pattern from discrete spots to overlapping diffraction disks.
Lateral Coherence Measurement: To quantify lateral coherence, the authors adapted a TEM-based technique using a twisted bilayer of graphene. In this geometry, two graphene layers with a specific twist angle ( $\beta$ ) act as diffraction planes. The relative rotation creates a lateral displacement in reciprocal space, causing electrons diffracted from the two layers to interfere when the diffraction disks overlap. The visibility of the resulting interference fringes is directly related to the degree of lateral coherence at a specific spatial frequency defined by the twist angle and diffraction order.

Key Results

Diffraction Capability: The system successfully generated high-quality SAED maps from Au flakes and CBED patterns from graphene monolayers, validating the transition from parallel to convergent beam geometries at 30 keV.
Interference Pattern Observation: In twisted bilayer graphene samples, the team observed distinct interference fringes within overlapping diffraction disks. The orientation and periodicity of these fringes matched theoretical calculations for a perfectly coherent beam, confirming the experimental geometry.
Quantitative Coherence Values: By analyzing line scans perpendicular to the interference fringes and computing their Fourier transforms, the authors extracted fringe visibility values:
- For a transverse wave vector separation of 0.031 Å⁻¹ (first diffraction order), the visibility was approximately 60%.
- For a separation of 0.053 Å⁻¹ (second diffraction order), the visibility dropped to 20%.
Coherence Scale: The authors calculated that the 60% visibility corresponds to a lower limit for the degree of lateral coherence over 5% of the e-beam diameter. They note that this is a conservative estimate, as factors such as inelastic scattering, specimen contamination, and unknown exact layer counts likely reduce the observed visibility further.

Significance and Claims
The paper presents a proof-of-concept demonstrating that 4D-STEM in a SEM can be used to quantify the lateral coherence of low-energy electron beams. The authors claim that the observed coherence values (60% over 5% of the beam diameter) are sufficient to enable future quantum-coherent electron-light-matter interaction experiments, such as single-electron/single-photon coincidence measurements.

The work highlights that while the current measurement samples only a fraction of the full wave vector range, the technique successfully characterizes key beam parameters (semi-convergence angle and lateral coherence) without requiring modifications to the standard SEM column. The authors suggest that this approach, combined with cathodoluminescence spectroscopy, could facilitate the correlation of structural and optical properties, ultimately advancing the study of quantum electron-photon coupling in the SEM environment.

The Problem: Is the Beam "In Sync"?

The Solution: A New Trick with Twisted Graphene

What They Found

Why This Matters (According to the Paper)

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