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Substrate-Assisted Cathodoluminescence

This paper demonstrates a minimally invasive cathodoluminescence technique where substrate-generated electrons excite diamond color centers, enabling the detection of extremely low effective currents (down to 0.1 pA) through photon-correlation experiments.

Original authors: Sven Ebel, N. Asger Mortensen, Sergii Morozov

Published 2026-04-01

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CC BY 4.0

Original authors: Sven Ebel, N. Asger Mortensen, Sergii Morozov

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 delicate, glowing firefly (a quantum emitter) that you want to study. Usually, to make it glow, you shine a super-bright, high-powered spotlight (an electron beam) directly on it. But here's the problem: that spotlight is so intense and hot that it might burn the firefly or damage its delicate wings.

This paper introduces a clever, gentler way to light up these fireflies without touching them directly. Instead of shining the light on the firefly, the researchers shine the light on the ground right next to it.

Here is how the magic works, broken down into simple concepts:

1. The "Bouncing Ball" Effect (The Substrate)

Think of the electron beam as a stream of tiny, fast-moving billiard balls.

Direct Excitation: If you shoot the balls directly at the firefly, they hit it hard and make it glow. But this is rough on the firefly.
Indirect Excitation (The New Trick): The researchers aim the stream of balls at the table (the substrate) next to the firefly. When the balls hit the table, they bounce off.
- Some bounce back with a lot of energy (called Backscattered Electrons).
- Some bounce off weakly and scatter everywhere (called Secondary Electrons).

The paper discovered that these bouncing balls (specifically the high-energy ones) travel through the air, hit the firefly, and make it glow just as well as if you had shot the firefly directly. But because the firefly isn't being hit by the main stream, it stays safe and unharmed.

2. The "Floor Material" Matters

The researchers found that the type of floor (substrate) you use changes how the balls bounce.

Soft, light floors (like Silicon): The balls sink in a bit, bounce around a lot, and come back up in a wide, fuzzy cloud. This creates a wide, gentle glow around the firefly.
Hard, heavy floors (like Germanium or Gold): The balls hit the hard surface and bounce back immediately, like a superball on concrete. They don't travel as far, creating a tight, sharp, but intense glow right near the impact point.

It's like throwing a tennis ball on a carpet (it spreads out) versus throwing it on a concrete wall (it bounces back sharply).

3. The "Crowded Room" Detective Work

How did they know the firefly was being lit by these tiny, scattered bounces and not by some other invisible force? They used a clever trick involving crowds.

Imagine the firefly is a person in a room.

If you have a huge crowd of people shouting at once (a strong electron beam), the person is overwhelmed, and the noise is chaotic but steady.
If you have a tiny crowd (a very weak beam), the person only speaks when a few people shout at the exact same time. The silence between shouts is long, but when they do speak, it's very synchronized.

The researchers used a special camera to listen to the "shouts" (photons) from the firefly. They found that when using the "indirect" method (bouncing off the floor), the firefly was being hit by a tiny, tiny crowd of electrons—so small it's like a single drop of water compared to a firehose.

By measuring how "synchronized" the light was, they could calculate exactly how weak the current was. They found it was incredibly low—down to 0.1 picoamperes. To put that in perspective, that's a billion times weaker than the current in a standard LED lightbulb.

Why This is a Big Deal

This discovery is like finding a way to examine a fragile snowflake under a microscope without melting it.

Safety: It allows scientists to study super-sensitive quantum materials that would normally be destroyed by the harsh electron beams used in standard microscopes.
Precision: It gives them a way to "tune" the light. By changing the floor material or how far away they aim the beam, they can control exactly how much energy the sample gets.
New Tool: It turns a standard microscope into a gentle, non-invasive probe for the future of quantum technology.

In a nutshell: The researchers figured out how to make tiny, glowing diamonds shine by bouncing electrons off the table next to them, rather than hitting the diamonds directly. This keeps the diamonds safe, and by listening to the rhythm of the light, they proved they are using a whisper-quiet amount of energy to do it.

1. Problem Statement

Cathodoluminescence (CL) microscopy is a powerful tool for characterizing quantum emitters, plasmonic resonators, and photonic nanostructures by combining spectral, spatial, and temporal information. Traditionally, CL relies on direct excitation, where a high-energy primary electron beam penetrates the sample to excite emitters.

Limitation: Direct excitation often involves high electron currents that can damage sensitive quantum emitters or induce unwanted heating.
Gap: While "indirect excitation" (mediated by secondary electrons (SEs) or backscattered electrons (BSEs) from a substrate) has been observed, the physical mechanisms, spatial extent, and quantitative impact on emitter excitation currents remain poorly understood. Specifically, it is unclear how substrate properties influence this process and whether it can be used as a low-damage excitation strategy.

2. Methodology

The authors employed a combination of experimental CL microscopy, photon-correlation spectroscopy, and Monte Carlo simulations to investigate indirect excitation.

Sample System: Diamond crystals containing Silicon Vacancy ( $SiV^-$ ) color centers were used as robust, bright, and stable local probes.
Experimental Setup:
- A Scanning Electron Microscope (SEM) equipped with a parabolic mirror for CL collection.
- Detection via a spectrometer and a Hanbury Brown–Twiss (HBT) interferometer for second-order autocorrelation ( $g^{(2)}(\tau)$ ) measurements.
Excitation Geometries:
- Direct Excitation: The electron beam impinges directly on the diamond.
- Indirect Excitation: The electron beam is positioned several micrometers away from the diamond (e.g., 2 µm), ensuring no direct beam interaction. Excitation is driven solely by electrons generated in the substrate.
Substrate Variation: Experiments were conducted on various substrates with different atomic numbers ( $Z$ ) and densities ( $\rho$ ), including Silicon ($Si$), Germanium ($Ge$), Graphite, Gold ($Au$), and thin $Si_3N_4$ membranes on bulk $Si$.
Quantification Strategy: The authors utilized the photon bunching amplitude ( $g^{(2)}(0)$ ) as a proxy for excitation current. Since $g^{(2)}(0)$ is inversely proportional to the excitation current ( $I$ ) in solid-state luminescent systems ( $g^{(2)}(0) \propto 1/I$ ), measuring the bunching allows for the extraction of the effective current experienced by the emitter, even when the nominal beam current is high.

3. Key Contributions

Mechanism Identification: The study definitively identifies Backscattered Electrons (BSEs) as the dominant driver of substrate-assisted indirect CL, rather than low-energy Secondary Electrons (SEs).
Substrate Dependence: The research establishes a direct correlation between substrate material properties ( $Z$ and $\rho$ ) and the spatial distribution of indirect excitation.
Quantitative Current Estimation: The authors propose and validate a method using photon-correlation spectroscopy to quantify effective excitation currents in indirect regimes, revealing currents orders of magnitude lower than the nominal beam current.
Low-Damage Strategy: The work demonstrates that indirect excitation offers a "gentle" alternative for probing sensitive emitters, reducing damage risks significantly.

4. Key Results

Mechanism of Indirect Excitation:
- When the beam hits a substrate (e.g., bulk Si) near a diamond on a thin membrane, CL is observed from the diamond despite no direct beam contact.
- BSEs vs. SEs: SEs have low energy (<50 eV) and short escape depths, limiting their range to nanometers. In contrast, BSEs retain significant kinetic energy (keV range) and can travel micrometers. Monte Carlo simulations confirmed that BSEs are responsible for the long-range excitation.
- Energy Dependence: At high beam energies (30 keV), BSEs travel micrometers, exciting distant emitters. At low energies (5 keV), the BSE range shrinks, and excitation becomes negligible unless the beam is very close.
Spatial Distribution and Substrate Material:
- Low-Z/Low- $\rho$ Substrates (e.g., Si, Graphite): Electrons penetrate deeper and undergo multiple scattering events, resulting in a Gaussian-like spatial intensity distribution of the induced CL.
- High-Z/High- $\rho$ Substrates (e.g., Ge, Au): Electrons scatter closer to the surface with fewer events, resulting in an exponential-like spatial decay of the CL intensity.
- This behavior was validated across Si, Ge, Graphite, and Au substrates.
Photon Correlation and Effective Current:
- Under indirect excitation, the photon bunching amplitude ( $g^{(2)}(0)$ ) increased dramatically (e.g., from ~1.6 in direct excitation to ~64 in indirect excitation at the same nominal beam current).
- This increase signifies a massive reduction in the effective excitation current.
- By fitting the $g^{(2)}(0)$ vs. current relationship, the authors estimated the effective excitation current experienced by the emitter to be as low as 0.1 pA, despite the instrument operating at ~240 pA to 1.4 nA.
- The effective current decays exponentially with distance from the beam impact point, mirroring the CL intensity profiles.

5. Significance

Minimally Invasive Probing: The ability to excite quantum emitters with effective currents as low as 0.1 pA opens new avenues for studying radiation-sensitive materials (e.g., biological samples, fragile 2D materials, or single-photon sources) without the damage associated with direct high-current electron beams.
New Excitation Modality: This work transforms "substrate noise" (indirect excitation) into a tunable, controllable excitation source. By selecting specific substrates (Z and $\rho$ ), researchers can engineer the spatial profile (Gaussian vs. Exponential) of the excitation field.
Advanced Characterization Tool: The use of photon-correlation spectroscopy to quantify effective currents provides a robust, non-invasive metric for understanding electron-sample interactions in complex geometries, bridging the gap between CL intensity and actual excitation dynamics.

In conclusion, the paper establishes Substrate-Assisted Cathodoluminescence as a distinct and powerful excitation regime driven by BSEs, offering a highly sensitive, low-damage method for the spatially resolved investigation of quantum emitters.