Can a standard scanning electron microscope reveal very fast mechanical motion? The authors time-tag secondary electrons and sort repeated drive cycles into phase-resolved movies of quartz and an AFM cantilever assembly. The quartz benchmark demonstrates about 3 nm spatial and 3 ns temporal tracking jitter. Effective frame spacing is independent of raster speed; reconstruction requires reproducible motion and takes minutes to hours.

Small Methods · 2026 / An interactive research journey

A slow electron scan can reconstruct snapshots less than a nanosecond apart. The secret is to remember when each electron arrived—and to observe the same motion again and again.

Explore original movies, build an acquisition, edit a beam model, and challenge what a movie can tell you.

Calculated frame spacing 96 frames at 12.588 MHz

Reported tracking jitter Quartz benchmark, not every specimen

Reported scan duration A fast reconstruction from a slow scan

01 / A field of motion

A moving shape tells more than a frequency.

A tiny cantilever rides on a quartz tuning fork. Choose a resonance and move through its cycle. Some motion is invisible to the electrical measurement.

Choose 49 kHz . Watch the cantilever move, then look for its peak in the electrical trace.

Fork 1 · 32.2 kHz

Original supplement · 100 phases per cycle. Playback is slowed. Horizontal and vertical scales differ.

A line through the movie

One image row, across the whole cycle. Drag down to travel through phase; move the sampling row to inspect another place.

Rightmost bright run of at least two pixels. Excursion is estimated from rendered images, not raw counts. Gray stripes are retained from the source.

Another instrument · Figure 3D

Does the electrical trace see it?

S₂₁ is electrical transmission through the assembly. This is the original local frequency window, enlarged.

The five windows are separate experiments; they are not one continuous frequency sweep. The source’s low-resolution plot is retained without inventing extra samples.

A full image reveals where a mode moves. Now follow this response into an acquisition or a mechanical model.

The three fork-driven responses have published shape comparisons.

A cantilever is a flexible beam held at one end. Here it is mounted at 35° to a quartz tuning fork. Driving the fork can carry and bend the attached beam; driving a cantilever resonance reveals its own response.

The stage was tilted 35° for a sharp top-surface view. The measured movies show projected in-plane motion. These are different driven experiments, aligned by relative phase—not simultaneous modes in one recording.

Figure 3C crop · original SEM image courtesy of QZabre, as credited in the paper. Figure 3A explains the orientation.

Another specimen. Another scale.

On quartz, a gold particle becomes a marker for motion far smaller—and faster—than the cantilever’s.

A 25 nm gold marker on a driven quartz crystal. The trajectory uses Supplementary Table 1. The small circle has a 3 nm radius, a reference for the reported spatial residual scale. The arrow indicates velocity direction only. The circle is not a new measurement or a confidence interval.

Two nearby resonances move the surface in different directions. An elliptical path becomes almost a straight line when the x and y phases match.

The paper reports about 3 nm spatial and 3 ns temporal tracking jitter. The main text gives the second frequency as 12.612 MHz; this reconstruction follows the supplement’s 12.614 MHz table.

02 / Weaving repeated time

A slow scan. A fast reconstructed world.

The beam stays at one pixel while the specimen repeats thousands or millions of cycles. Sorting electron arrivals by the drive phase gives that pixel a place in every movie frame.

Sort the arrivals. Then increase the number of frames. Which changes: timing, counts, or scan time?

A synthetic experiment at the selected source frequency

One pixel remembers a cycle

Synthetic single-pixel arrivals, with a bright edge crossing twice per cycle. The same event list is rebinned when the frame count changes. The highlighted image pixel uses that list; other pixels use illustrative count statistics.

Before phase sorting

Image statistics use a synthetic background of 1,000 electrons/s and a bright-edge peak of 20,000 electrons/s. Native timing bins in the paper are 82.3 ps; its gold-particle benchmark gives roughly 3 ns tracking jitter. A finer output interval does not establish finer physical accuracy. This example does not model saturation or recover the authors’ raw data.

Reference acquisition: the 522 kHz, 200 × 200 cantilever movie used 250 ms dwell plus 20 ms overhead per pixel, taking about three hours. Figure 5D explains the phase reconstruction.

A continuous primary beam scans the specimen. Secondary electrons reach a fast multi-channel plate detector. A time-to-digital converter records timing relative to the periodic drive reference. Reconstruction assigns those events to phases.

The source reports 82.3 ps TDC bins, <85 ps specified detector jitter, 250 ps drive-reference jitter, and an estimated 600 ps flight-time spread plus angle effects. These different quantities do not form an independently validated Gaussian error budget.

03 / From a shape to mechanics

One beam. More than one explanation.

Cutouts change both inertia and bending stiffness. Fit one effective modulus, hold it across three responses, and inspect what the model still misses.

Fit one response. Keep the same modulus for another. Now thin one section to 80% and inspect how stiffness changes.

The perforated specimen

Actual silhouette from Figure 4A. Edits change an effective section profile; the cutout drawing itself stays as the source reference. The model is a proposed specimen when edited.

Confront the observed shape

Source shape samples Recreated prediction

All three profiles helped reconstruct their base inputs at 65 GPa. Comparing them with a shared modulus is not independent validation. Errors here are ours, not the authors’ reported R².

The edit beneath the image

Mass changes once. Stiffness changes cubically.

Under the supplement’s effective-section model, μ = whρ and I = wh³/12. A local edit changes the mathematical section; the cutout silhouette remains a reference.

Mass per length Bending stiffness

Start at 130 GPa, the tabulated silicon value cited by the supplement. The paper uses Eeff = 65 GPa.

We solve a 24-element Euler–Bernoulli beam with prescribed base translation and rotation, using I = wh³/12 and μ = whρ, w = 10 μm, ρ = 2,330 kg/m³ and approximate I(x) digitized from Figure 4B. The laboratory-frame dynamic equation is [(1 + iη)K − ω²M]û = 0 with the driven base prescribed, η = 0.015. Motion is shown as Re[û exp(iφ)]; the elastic moment is −EIu″. Phase zero gives the in-phase response used in the comparison.

A 1.5% structural loss regularizes resonance in this exploratory model; it is not measured damping. Geometry and base inputs are reconstructed, so this is not an exact reproduction of the authors’ model. The paper’s Figure 4 caption and supplementary mass relation differ; we use the explicit supplementary equations.

The original shared 65 GPa fit has reported R² of 0.999, 0.996 and 0.950. Effective modulus can absorb uncertain geometry, clamp compliance and omitted torsion. It is not a measurement that silicon’s intrinsic modulus changed. Bending moments shown here are model-derived, not measured forces.

04 / A test of trust

A smooth movie can hide different histories.

Phase folding asks what happens at a given point in a repeated drive cycle. Change the specimen’s repeatability and inspect what that same reconstruction would conceal.

Individual cycles and their average

The original reconstruction assumes deterministic, repeatable behavior. These altered cycles are synthetic tests of that assumption.

Changes here also alter the synthetic arrivals in “Assemble time.”

Carry a question back to the paper

What can you now claim?

Choose a statement. The experiments you changed determine which part of it you can defend.

Original research & evidence

Based on Nanosecond, Nanometer Movies of MEMS/NEMS Dynamics in a Standard SEM Using Time‐Tagged Secondary Electrons.

Joel Rehmann, Constantin Schalast, Karsten Kunze, Jan Rhensius & Yves Acremann · Small Methods 10 (19), 2026 · DOI: 10.1002/smtd.71029.

Original figures and supplementary movie: CC BY 4.0. Cropping, spatial resampling and approximate figure digitization are adaptations. Figure 3 assembly imagery is credited by the paper to QZabre. Graphical abstract: generated conceptual illustration, informed by the paper; its image tiles are illustrative.

The five cantilever movies and electrical windows are original evidence. Quartz trajectories reconstruct published fits. The beam model is our approximate recreation. Acquisition events and altered cycle histories are illustrative experiments. Authors’ data and analysis collection · raw inputs were unavailable during this reconstruction.