🔬 mesoscale physics

Sub-diffraction-resolved spatial distribution of emitting excitons in STM-induced luminescence of 2D semiconductors via Richardson-Lucy deconvolution

This paper demonstrates that Richardson-Lucy deconvolution of scanning tunneling microscopy-induced luminescence images enables sub-diffraction-resolved mapping of exciton spatial distributions in 2D semiconductors like $\mathrm{WSe_2}$ and $\mathrm{WS_2}$ , revealing critical dependencies on tunnel current and unexpected long-range emission from hot spots.

Original authors: Elysé Laurent, Ricardo Javier Peña Román, Sarah Miller, Aditi Raman Moghe, Etienne Lorchat, Séverine Le Moal, Elizabeth Boer-Duchemin, Luiz Fernando Zagonel, Stéphane Berciaud, Eric Le Moal

Published 2026-07-09

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Elysé Laurent, Ricardo Javier Peña Román, Sarah Miller, Aditi Raman Moghe, Etienne Lorchat, Séverine Le Moal, Elizabeth Boer-Duchemin, Luiz Fernando Zagonel, Stéphane Berciaud, Eric Le Moal

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 are trying to find a single firefly that just landed on a dark, flat leaf. You have a super-powerful flashlight (the microscope) that can see the leaf, but it's a bit fuzzy. When the firefly lands, your flashlight shows you a glowing blob. The problem is, that blob is blurry. It looks like a big, soft circle of light, but you don't know exactly where the firefly is standing inside that circle, or if there are other fireflies nearby that your fuzzy light is mixing together.

For a long time, scientists studying 2D materials (which are sheets of atoms so thin they are almost flat) faced this exact problem. They used a tiny, sharp metal needle (an STM tip) to zap the material with electricity, creating glowing particles called "excitons." They could see the light, but because their "flashlight" was blurry, they couldn't tell if the light was coming from just under the needle or if the glowing particles had run away to other spots on the leaf.

In this study, the researchers acted like digital detectives. They didn't just look at the blurry photo; they used a clever computer trick called Richardson-Lucy deconvolution to "un-blur" the image. Think of it like taking a photo of a rainy window and using software to mathematically reverse the raindrops, revealing the sharp city lights behind them. By feeding the computer a perfect model of how their microscope blurs light, they could mathematically peel back the fuzz and see the true shape of the glowing spots.

The First Discovery: The "Runaway" Glow
When they zapped a sheet of tungsten diselenide (WSe2) with their needle, they found something surprising. The size of the glowing blob wasn't fixed. When they turned up the "volume" of the electricity (the tunneling current) from 0.5 nA to 2.0 nA, the glowing area got bigger.

Specifically, the width of the glow (measured as the Full Width at Half Maximum, or FWHM) grew from about 0.12 µm to 0.14 µm along one direction and 0.10 µm to 0.18 µm along the other. The authors suggest this happens because the electric field around the needle changes as the current changes, kind of like how a stronger wind might push a dandelion seed further before it lands. They are quite sure this is happening because they measured it directly, but they note that the particles don't run away because they are bumping into each other (which would happen if there were too many), but because of this electric push.

The Second Discovery: The "Ghost" Fireflies
Here is where it gets really cool. In a different material, tungsten disulfide (WS2), they saw something that confused everyone before. When they zapped the material, they saw bright spots of light appearing micrometers away from the needle—sometimes as far as 8.4 µm away!

Before this paper, people thought these distant spots were the excitons (the glowing particles) running all the way across the leaf before dying. But the authors say: No, that's not it.

They argue that if the particles were just running, the spot under the needle should be the brightest, and the light should get dimmer the further you go. But in their "un-blurred" photos, some of these distant spots were actually brighter than the spot right under the needle! That doesn't make sense if they are just running away.

Instead, the authors propose a different story. They suggest that the electricity from the needle shoots out invisible electrons that travel across the leaf. These electrons are looking for a partner to pair up with. Usually, the leaf doesn't have enough partners (holes) nearby. But at specific "traps"—like tiny folds or wrinkles in the leaf (called nanofolds)—there are holes waiting. When the traveling electrons finally find these holes at the folds, they pair up and glow.

So, the distant lights aren't the original particles running; they are new lights turning on far away because the electrons traveled there to find a partner. The "blurry" microscope made it look like the light was spreading out smoothly, but the deconvolution showed it was actually popping up at specific, distant locations.

How Clear is the Picture?
The researchers are very confident in their "un-blurring" math. They tested two different computer scripts to make sure they weren't creating fake patterns. One script worked better than the other. Using the best script, they could see glowing spots that were only about 0.105 µm wide.

To put that in perspective, the limit of what a normal microscope can see (the diffraction limit) is about 0.25 µm. They managed to see details that are two to three times smaller than what the microscope should theoretically allow. They even saw two distinct spots separated by 0.295 µm, which a normal microscope would have merged into one big blob.

What They Didn't Find
It's important to note what they didn't see. In the first material (WSe2), they didn't see these distant "ghost" spots at all. The light stayed right under the needle. This proves that the distant spots aren't a universal rule for all 2D materials; they depend on the specific material and the settings of the needle.

Also, they ruled out the idea that the distant spots were just a trick of the blurry microscope. By mathematically removing the blur, they showed that the distant spots are real, sharp features, not just the tail end of a big, fuzzy glow.

The Bottom Line
This paper shows that by using a sharp needle to zap 2D materials and a smart computer algorithm to clean up the blurry photos, scientists can finally see exactly where the light is coming from. They found that the size of the glow changes with the electric current, and that sometimes, the light appears far away from the source not because the particles ran there, but because the electricity traveled there to find a partner. It's like realizing the fireflies you saw far away weren't the ones you startled, but new ones lighting up because your flashlight sent a signal that traveled across the leaf to wake them up.

Technical Summary: Sub-diffraction-resolved spatial distribution of emitting excitons in STM-induced luminescence of 2D semiconductors via Richardson-Lucy deconvolution

Problem Statement
Scanning tunneling microscopy-induced luminescence (STML) allows for the investigation of optical properties in two-dimensional (2D) semiconductors at the nanoscale by utilizing the tunneling current as a highly localized excitation source. However, a critical limitation in most STML applications is that the spatial distribution of the emitted light relative to the excitation point remains unresolved. Standard STML "photon mapping" techniques record the total integrated light while scanning the tip, generating maps that lack information on the actual spatial distribution of emitters (excitons). This obscures key physical insights regarding exciton transport, interactions with injected charge carriers, and the mechanisms governing luminescence. While wide-field optical microscopy combined with STML can capture real-space images, the spatial distribution of emitters is typically blurred by the diffraction limit of the optical microscope (the Point Spread Function, or PSF), making it difficult to resolve features smaller than the diffraction limit, especially when exciton diffusion lengths are short.

Methodology
The authors address this challenge by applying an iterative deconvolution algorithm, specifically the Richardson-Lucy (RL) algorithm, to real-space optical microscopy images of STML from monolayer tungsten diselenide (WSe $_2$ ) and tungsten disulfide (WS $_2$ ).

Experimental Setup: The experiments utilize a commercial STM head mounted on an inverted optical microscope equipped with a high-numerical aperture (NA = 1.49) oil-immersion objective. Samples are mechanically exfoliated monolayer TMDs on indium tin oxide (ITO)-coated glass. Light is collected in transmission.
PSF Modeling: A critical component of the method is the accurate definition of the PSF. Unlike standard fluorescence microscopy where emitters are often isotropic, the authors model the emitters as spin-bright excitons in TMD monolayers. These have transition dipole moments oriented in-plane and emit circularly polarized photons. The PSF is numerically simulated by coherently summing the emission of two perpendicular in-plane electric dipoles, accounting for the dielectric environment (ITO layer and glass substrate) and the experimentally measured spectral distribution of the emitted light.
Deconvolution Process: The authors employ the RL algorithm to estimate the most likely object (spatial distribution of emitters) from the blurred, noisy experimental image. They compare two implementation scripts: one using direct 2D convolution and another using Fourier transform products. To overcome the limitations of native pixel sampling (which is insufficient for accurate width estimation), the experimental images and the simulated PSF are upsampled by a factor of 10 via interpolation before deconvolution.

Key Results
The application of RL deconvolution to STML data yields two primary findings regarding the physics of excitons and charge carriers in 2D semiconductors:

Current-Dependent Spatial Distribution: In monolayer WSe $_2$ , the spatial distribution of emitters around the excitation source is not static. The full width at half maximum (FWHM) of the emitter distribution increases linearly with the tunneling current setpoint (from ~0.12 µm at 0.5 nA to larger values at 2.0 nA). The authors attribute this broadening not to exciton-exciton interactions (which are negligible at these densities) but to the interaction of excitons with the radial electric field and potential gradient around the tip, both of which intensify as the tip-sample distance decreases with higher current setpoints.
Origin of Distant Emission Hotspots: In monolayer WS $_2$ , the authors observe emission "hotspots" located several micrometers away from the STM tip. Previous interpretations attributed such features to long-range exciton diffusion. However, the RL-deconvolved images reveal that the apparent spatial overlap between the tip emission and distant hotspots in raw data is an artifact of the PSF's long tail. The deconvolved data shows that the actual emitter distribution under the tip is compact (~0.1 µm FWHM). The authors propose an alternative mechanism for the distant hotspots: injected electrons diffuse laterally from the tip and recombine radiatively with holes trapped at defects (such as nanofolds or edges) in the monolayer. This explains why hotspots appear only at specific biases (e.g., 4 V vs. 2 V) and are spatially correlated with sample defects rather than following a simple diffusion decay profile.

Significance and Claims
The paper claims to resolve the spatial distribution of emitting excitons beyond the diffraction limit of light by combining STML with wide-field optical microscopy and iterative deconvolution. The significance of this work lies in:

Methodological Advancement: It demonstrates that RL deconvolution, when paired with a physically accurate PSF model for in-plane dipoles, can extract sub-diffraction spatial information from STML experiments, a capability previously unattained in this field.
Physical Insight: It corrects misconceptions regarding STML on 2D semiconductors. Specifically, it clarifies that the spatial distribution of emission is sensitive to tunneling current parameters and that distant emission hotspots are likely due to electron diffusion and defect-mediated recombination rather than long-range exciton diffusion.
Fundamental Understanding: The technique provides a new tool for investigating elementary optical and electronic processes in real space, offering insights into exciton transport, charge carrier dynamics, and the interaction between injected carriers and material defects.

The authors maintain a modest tone regarding the resolution limits, noting that the effective resolution is constrained by noise levels, photon counts, and algorithm convergence criteria, and that the extracted FWHM values should be considered upper limits. They conclude that this approach enables the study of mechanisms in tunneling-current-driven TMD-based nanodevices that are inaccessible to conventional photon-mapping STML techniques.

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