E33 · X-ray microanalysis

STEM-EDS: Nanochemical Maps

Does a sharper electron probe guarantee a sharper chemical map? No. The beam spreads as it passes through the foil, so X-rays come from a wider region than the probe itself. Peaks from different elements can overlap, part of the X-rays is absorbed on the way out, and only a limited number of photons is counted. The map ends up blurrier than the probe, and no processing after the scan can undo that mixing.

Scan a thin simulated foil that contains a vanadium-rich nanodomain, storing an X-ray energy spectrum at every probe position. Pull region spectra and line profiles from the stored data, and compare the raw energy windows with a composition estimate corrected for the known response.

Recorded region spectrum counts $\text{—}$

Fitted vanadium atomic fraction $\text{—}$

Conditional counting standard error $\text{—}$

Assumed effective FWHM $\text{—}$

More measurements and target

Selected stored pixels $\text{—}$

Horizontal drift during full raster $\text{—}$

Raster acquisition duration $\text{—}$

Incident electron areal dose $\text{—}$

Composition response assumption $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

More examples

Specified foil thickness

t

80\,\mathrm{nm}

Dwell per scan pixel

\tau

0.05\,\mathrm{s}

Sample drift along horizontal axis

v_d

0\,\mathrm{\frac{nm}{s}}

Absorption response: 0 off, 1 on

0

Advanced settings

Incident beam current

I

100\,\mathrm{pA}

X-ray detector solid angle

\Omega

0.4\,\mathrm{sr}

Take-off angle above foil

\alpha

20\,\mathrm{^\circ}

EDS response FWHM

130\,\mathrm{eV}

Incident probe FWHM

1\,\mathrm{nm}

Stored region center: horizontal

x_s

0\,\mathrm{nm}

Stored region center: vertical

y_s

0\,\mathrm{nm}

Stored region radius

r_s

6\,\mathrm{nm}

Learning goal and model limits

Make a prediction, then test it

Does a sharper electron probe guarantee a sharper chemical map?

Target: place the selected region inside the nanodomain and use an absorption-corrected fit. Keep the foil thickness at or below 60 nm, the probe FWHM at or below 2 nm and the total drift at or below 1 nm. You need more than 2,000 counts in the region, an error below 0.04 and a fitted vanadium fraction within 0.05 of 0.55.

Model assumptions

This is a teaching model of a thin foil at a fixed beam energy of 200 keV, not a calibrated atomic-column analysis. The field is 60 nm square with 2.5 nm pixels and holds a predefined cylindrical nanodomain. Titanium and vanadium line energies come from NIST; relative yields are assumed, matrix attenuation lengths are fixed and the EDS response is Gaussian. X-ray emission grows linearly with foil thickness. Self-absorption on the way to the collector above the foil is found by averaging escape over a uniform emission depth. The Gaussian beam spread grows with thickness; its coefficient is an invented teaching value, and no multiple-scattering calculation is done. The sample drifts at a constant rate, applied at the time each raster pixel is recorded; flyback is not included. The correction uses the given thickness and the known response. It cannot undo spatial mixing or work out an unknown thickness. Nonnegative spectral fits use the stored counts. Their error estimate assumes high counts and a correct model, and it leaves out model uncertainty and the effects of a fraction sitting at zero. Each count map has its own logarithmic color scale. The fitted composition uses a fixed linear scale and grays out pixels with fewer than 30 counts. The 3D view exaggerates the foil thickness. Dynamical channeling, calibrated cross sections, shadowing, fluorescence, beam damage, dead time and pile-up are not modeled. Dose here means incident electrons per pixel area; it does not predict damage.

Physics tutorial

STEM-EDS: Nanochemical Maps

BackgroundIn this Lab the probe records a full X-ray spectrum at every position on a thin simulated foil that contains a vanadium-rich nanodomain. The electron beam spreads as it crosses the foil, and some X-rays are absorbed on their way out to the detector.

Why it mattersYour task is to measure the inside of the nanodomain with an absorption-corrected fit. Keep the foil thickness at or below 60 nm, the probe FWHM at or below 2 nm and the total drift at or below 1 nm. You need more than 2,000 counts in the region, an error below 0.04 and a fitted vanadium fraction within 0.05 of 0.55.

Start with the essentials

Focus question: Does a sharper electron probe guarantee a sharper chemical map?
One-sentence intuition: A chemical map reflects probe spreading, spectral overlap, self-absorption and counting precision all at once. Reprocessing the stored counts changes how you interpret them, but it cannot add photons or undo spatial mixing.

Core mathematical model

Escape fraction averaged over the foil depth

A=\frac{1-e^{-u}}{u},\qquad u=\frac{t}{\ell\sin\alpha}

Beer–Lambert attenuation averaged over a uniform emission depth gives the fraction of X-rays that leave the flat foil toward a collector above it.

Fitted vanadium fraction

\widehat c_V=\frac{a_V}{a_{Ti}+a_V}

The fraction comes from the fitted vanadium and titanium amplitudes. The response used in the fit can include the known absorption correction, but nothing in it undoes probe spreading.

Incident dose

D=\frac{I\,\tau}{e\,A_{pixel}}

Dose is the number of incident electrons per scan-pixel area. This Lab does not use it to estimate damage.

Common difficulties

Window brightness needs a response model

Typical misconceptionWherever the vanadium window is bright, that is exactly where the vanadium is.

Better mental modelA window map shows photon counts, not concentration. Those counts depend on probe spreading, spectral overlap, self-absorption and counting precision. Reprocessing the stored counts changes the interpretation, but it does not add photons or reverse spatial mixing.

Run the experiment

01
Compare thin and thick foils
Switch between the thin and thick foil presets; the reference nanodomain stays the same.
What to observe: The thicker foil gives more photons, but the boundary in the count maps gets wider.
02
Reprocess the same data
Turn the absorption correction on and off, and move the selected region.
What to observe: The recorded cube does not change. The spectra and composition estimates are recalculated from the same pixels.
03
Separate the error sources
Try low counts, a broad probe and drift. Then check the target with a thin foil that does not drift.
What to observe: A small counting error does not make a measurement right if the signal is spatially mixed or the sample has drifted.