E24 · Low-voltage transmission

STEM-in-SEM: Through a Thin Specimen

How thin must a specimen be for a useful SEM transmission image? Thin enough that a good share of the electrons gets through at the low beam energy you have chosen. A thicker foil lets fewer through and blurs the image more. The detector collection angles then decide which transmitted electrons form the contrast.

Choose the beam energy, foil thickness and collection angles. Learn to tell weak transmission, probe blur and counting noise apart.

Selected virtual detector counts $\text{—}$

Selected-point transmitted fraction $\text{—}$

Signed contrast in separate audit regions $\text{—}$

Pooled ROI difference SNR $\text{—}$

More measurements and target

Selected sampled primary outcome total $\text{—}$

Simulated counts beyond 250 mrad $\text{—}$

Simulated removed-electron counts $\text{—}$

Assumed probe FWHM $\text{—}$

ROI 2 / ROI 1 mean count ratio $\text{—}$

Expected incident dose per scan pixel $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Incident beam energy

E

20\,\mathrm{keV}

Central normal wedge thickness

t

150\,\mathrm{nm}

Exposure per scan pixel

\tau

10\,\mathrm{\mu s}

Inner collection semi-angle

\beta_{in}

0\,\mathrm{mrad}

Outer collection semi-angle

\beta_{out}

20\,\mathrm{mrad}

Advanced settings

Probe convergence semi-angle

\alpha

5\,\mathrm{mrad}

Selected scan pixel index

k

528

Image display gain only

G

1

Learning goal and model limits

Predict · acquire · select · compare

How thin is thin enough?

Target: collect axial bright field. Reach a dark-ROI contrast of at least 0.1, a pooled difference SNR of at least 10 and a selected-point transmission of at least 30 percent, with an assumed probe FWHM of at most 5 nm.

Model assumptions

The counts are synthetic and come from a fixed random seed; they are not experimental data. A 32 by 32 raster stores 125 radial bins of 2 mrad at each point. Electrons that land outside this window, and electrons removed from the beam, are simulated and counted separately. The uniform disk of incident angles, the isotropic Gaussian spread of scattered electrons and the empirical attenuation lengths are teaching assumptions, not calibrated cross sections. A stated Gaussian probe blurs the finite specimen before counting. The labels BF, ABF and ADF describe only the collection angles: coherent phase contrast, dynamical diffraction, channeling and real ABF imaging of light atoms are not solved. Changing the virtual angles reuses the stored counts, and display gain never changes the numbers. Contrast is measured in regions fixed in advance; this is not elemental quantification. The hardware, the thickness and the lateral size of the specimen are each enlarged by a different amount. The apparatus shows one representative point on the axis and ignores nanometre scan movements. The SEM beam energy runs from 5 to 30 keV, with a 2 nm raster pitch over 64 nm. The carbon-like wedge varies from 0.6 to 1.4 times the chosen thickness and contains an invented inclusion of atomic number 29.

Physics tutorial

STEM-in-SEM: Through a Thin Specimen

BackgroundTo make a transmission image in an SEM, you choose the beam energy, the foil thickness and the collection angles. When the image is poor, you then work out whether weak transmission, probe blur or counting noise is to blame.

Why it mattersThe task is to see the inclusion in transmission. Collect from zero angle. Reach a dark inclusion contrast of at least 0.1, a pooled region difference SNR of at least 10 and a transmitted fraction of at least 30 percent at the selected point, with an assumed probe FWHM of at most 5 nm.

Start with the essentials

Focus question: How thin must a specimen be for a useful SEM transmission image?
One-sentence intuition: The angle range you choose decides which of the stored electrons make up the image.

Core mathematical model

Counts in angular bins

\begin{aligned}\mu_j&=\frac{I\tau}{e}\,p_j\\N_{\rm ann}&=\sum_{j\in\mathcal A}N_j\end{aligned}

Each virtual image adds up the stored radial counts in its chosen angular interval. The interval includes its lower edge but not its upper edge.

Assumed angular spread of scattered electrons

\begin{aligned}f(\theta)&=\frac{\theta}{s^2}\,e^{-\theta^2/(2s^2)}\\r&=L\tan\theta\end{aligned}

The isotropic Gaussian radial law stands in for a real transport calculation. The radius on the collector follows from the angle through the collector geometry shown on screen.

Contrast and noise in two known regions

\begin{aligned}C&=\frac{\overline N_2-\overline N_1}{\overline N_2+\overline N_1}\\\sigma_\Delta^2&=\frac{\sum_1N}{n_1^2}+\frac{\sum_2N}{n_2^2}\\S&=\frac{|\overline N_2-\overline N_1|}{\sigma_\Delta}\end{aligned}

This pooled difference uses the count statistics of two regions fixed in advance. It is not a per-pixel SNR, and it does not recover composition.

Common difficulties

A bright pixel is not a chemical analysis

Typical misconceptionAny annular image tells me directly which atoms are there.

Better mental modelThickness, the range of collected angles and probe overlap also change contrast. Phase effects at low angles need a coherent wave model, which this Lab does not include.

Run the experiment

01
Predict the contrast
Compare the separate specimen input with the bright-field image and the image from your selected angles.
What to observe: The known regions are there to check contrast. They are not a recovered chemical map.
02
Change the collection angles without re-acquiring
Change the inner and outer angles while watching the native histogram and the outcome totals.
What to observe: The virtual images change, but the native radial counts stay the same.
03
Try a setting that works
Use the Resolve the thin specimen preset and check the target. Compare the row profiles built from the counts.
What to observe: Read the signed contrast and the pooled difference SNR together.
04
Find the limits
Try low exposure, a broad probe and reversed bounds. Then increase the specimen thickness.
What to observe: Gain changes how the image looks. It cannot put back counts that were never collected or sharpen a blurred probe.

Core mathematical model

Counts in angular bins

Assumed angular spread of scattered electrons

Contrast and noise in two known regions

Common difficulties

A bright pixel is not a chemical analysis

Run the experiment

Predict the contrast

Change the collection angles without re-acquiring

Try a setting that works

Find the limits