E11 · Electron imaging / spectroscopy

SEM Secondary-Electron Topography

Rotate the side detector around a fixed terrace and three particles. Tilt the specimen, change working distance and landing energy, then compare the counted image with the true height map. The same terrain can look like a different object.

Flank mean counts $0$

Opposing-flank contrast $0\,\mathrm{\%}$

Contrast SNR $0$

Probe blur proxy $0\,\mathrm{nm}$

Assumed escape depth $0\,\mathrm{nm}$

Fixed grain height $0\,\mathrm{nm}$

Experiment task $\text{—}$

Geometric teaching model: assumed secondary yield, cosine collection, ray-tested occlusion and curvature edge enhancement. Beam blur is empirical; counts use seeded Poisson sampling with a Gaussian approximation above 40. No self-consistent detector field, charging or calibrated height inversion. The raster is presentation only.

Start with the essentials

Focus question: Does a brighter surface mean a taller surface?
One-sentence intuition: Detector geometry changes the image while the specimen stays fixed. Edge enhancement, visibility and counting statistics make brightness an ambiguous height measurement.

Core mathematical model

Electron counting

N_0=I\tau/e,\quad \bar N(x,y)=N_0Y(x,y)C(x,y)

Yield and collection are separate factors; the mean counts drive the image sampling.

Geometric collection proxy

C_{\mathrm{ET}}=(0.08+0.55\max(0,\mathbf n\cdot\mathbf d))V

The assumed visibility factor falls to 0.18 in a geometrically blocked direction; it is not a solved electrostatic collection efficiency.

Contrast and shot-noise test

c=\frac{|Y_1C_1-Y_2C_2|}{Y_1C_1+Y_2C_2},\quad \mathrm{SNR}=c\sqrt{2\bar N}

The two fixed flanks of the central grain define the reported contrast.

Common difficulties

Interpretation trap

Typical misconceptionA bright rim is a taller rim, and an SEM image is already a height map.

Better mental modelUse the fixed height reference and opposite-detector profile as counterexamples. Secondary-electron generation and collection both depend on geometry; quantitative height needs additional information.

Run the experiment

01
Predict the result
Predict which flank of the central grain will brighten when the detector turns by half a revolution. Compare Surface target and Opposite detector before changing the specimen tilt.
What to observe: Detector geometry changes the image while the specimen stays fixed. Edge enhancement, visibility and counting statistics make brightness an ambiguous height measurement.
02
Operate and check
Obtain at least 15 percent opposing-flank contrast, SNR at least 5, and a probe-blur proxy below 8 nm. Then reverse the detector and explain why the height map stays fixed.
What to observe: Use the numerical target, then compare the linked instrument and data views.
03
Explain the limitation
Switch to in-lens collection, then raise working distance and lower current. Identify directional shading, blur and counting noise separately.
What to observe: Geometric teaching model: assumed secondary yield, cosine collection, ray-tested occlusion and curvature edge enhancement. Beam blur is empirical; counts use seeded Poisson sampling with a Gaussian approximation above 40. No self-consistent detector field, charging or calibrated height inversion. The raster is presentation only.