E05 · Electron microscopy / specimen physics

Electron–Matter Signal Map

Change beam energy, atomic number, density and specimen thickness. Follow seeded primary-electron walks through the cutaway sample, switch emission pathways, and compare their source depths. Keep secondary electrons surface sensitive while transmitting at least half the primary beam.

Empirical range proxy $0\,\mathrm{nm}$

Stopped primary histories $0\,\mathrm{\%}$

Backscattered histories $0\,\mathrm{\%}$

Transmitted histories $0\,\mathrm{\%}$

SE 90-percent source depth $0\,\mathrm{nm}$

Auger 90-percent source depth $0\,\mathrm{nm}$

Assumed X-ray excitation edge $0\,\mathrm{keV}$

Experiment task $\text{—}$

Instrument settings

Electron–Matter Signal Map

Secondary electronsShow the corresponding signal path.Backscattered electronsShow the corresponding signal path.Characteristic X-raysShow the corresponding signal path.Auger electronsShow the corresponding signal path.CathodoluminescenceShow the corresponding signal path.Transmitted electronsShow the corresponding signal path.Transmitted energy lossShow the corresponding signal path.Landing energy

E_0

10\,\mathrm{keV}

Atomic number

Z

14

Mass density

\rho

2.33\,\mathrm{g\,cm^{-3}}

Specimen thickness

t

2000\,\mathrm{nm}

Transmit at least 50 percent of primary histories while keeping the modeled SE 90-percent source depth below 15 nm.

Teaching Monte Carlo: empirical Kanaya–Okayama range sets a continuous-slowing path budget; scattering is an invented random-walk kernel, not measured cross sections. Signal branches are schematic, not calibrated yields. SE and Auger escape lengths are assumed; CL requires a luminescent material. X-ray excitation uses a rough shell threshold. No quantitative compositional analysis.

Start with the essentials

Focus question: Where do the signals come from inside a specimen?
One-sentence intuition: A signal generated deep inside the specimen can be absorbed before reaching a detector. Transmission changes with thickness; surface escape remains shallow.

Core mathematical model

Empirical range scale

R=\frac{27.6AE_0^{1.67}}{\rho Z^{0.889}}\,\mathrm{nm}

Energy is in keV, density in grams per cubic centimetre. Atomic mass uses tabulated C, Si and Au values or an explicit proxy. The low-energy end is an extrapolation.

Escape weighting

w(z)\propto g(z)\exp(-z/\ell_{\mathrm{esc}})

Generated signal and escape probability are separate. The depth plot compares kernels normalized to their peaks, not absolute yields.

Common difficulties

Model boundary

Typical misconceptionA schematic image is a calibrated material prediction.

Better mental modelTeaching Monte Carlo: empirical Kanaya–Okayama range sets a continuous-slowing path budget; scattering is an invented random-walk kernel, not measured cross sections. Signal branches are schematic, not calibrated yields. SE and Auger escape lengths are assumed; CL requires a luminescent material. X-ray excitation uses a rough shell threshold. No quantitative compositional analysis.

Run the experiment

01
Predict
Predict which will transmit more: a silicon block or a thin foil. Compare their detected end-point fractions.
What to observe: A signal generated deep inside the specimen can be absorbed before reaching a detector. Transmission changes with thickness; surface escape remains shallow.
02
Tune and check
Transmit at least 50 percent of primary histories while keeping the modeled SE 90-percent source depth below 15 nm.
What to observe: The task checks quantitative readouts rather than visual brightness.
03
Explain the limit
Compare silicon and gold, then switch off each signal pathway. Explain why depth distributions differ even under the same beam.
What to observe: Teaching Monte Carlo: empirical Kanaya–Okayama range sets a continuous-slowing path budget; scattering is an invented random-walk kernel, not measured cross sections. Signal branches are schematic, not calibrated yields. SE and Auger escape lengths are assumed; CL requires a luminescent material. X-ray excitation uses a rough shell threshold. No quantitative compositional analysis.