E12 · Segmented SEM detection

BSE: Composition or Orientation?

Record both sides of a split detector. Calibrate their gains, switch between sum and difference, then rotate the specimen to separate material contrast, surface relief and prescribed channeling.

Stored left counts $\text{—}$

Stored right counts $\text{—}$

Count-derived material contrast $\text{—}$

Separate unchanneled input contrast $\text{—}$

Contrast error against input $\text{—}$

Contrast to representative pixel noise $\text{—}$

Selected count-derived asymmetry $\text{—}$

Prescribed mean channeling suppression $\text{—}$

Mean asymmetry error against geometry $\text{—}$

Incident dose per pixel $\text{—}$

Experiment target $\text{—}$

Predict · acquire · compare · explain

Can brighter grains prove a different composition?

Dwell per pixel

\tau

0.05\,\mathrm{ms}

Specimen rocking tilt about transverse axis

\alpha

8\,\mathrm{^\circ}

Relief amplitude multiplier

a

1

Actual right-sector count sensitivity

g_R

1.3

Apply known gain calibration: 1 on

c

0

View: 0 sum, 1 difference, 2 left

m

2

Selected stored pixel index

k

528

Derived-image display gain only

G

1

Target: use the calibrated sum away from strong grain channeling. Material contrast error at most 0.03, asymmetry mean error at most 0.05, representative pixel CNR at least 8 and prescribed mean channeling suppression at most 3 percent.

Seeded synthetic counts on a 32 by 32 raster, 20 nm pitch, 640 nm field and fixed 20 pA current. Dwell is per pixel; collection efficiency is fixed at 15 percent. Poisson counts below expectation 40 use a normal approximation above. Hardware and rays are schematic; the source, exposed face and same-face collectors are connected. Display gain and selected pixel reuse stored counts. No Monte Carlo transport, real detector calibration, contamination, damage kinetics or expert certification. Two prescribed materials have atomic numbers 14 and 29, each with alternating grain orientations at minus and plus 8 degrees. The monotone yield law and Gaussian rocking dips are declared teaching assumptions, not material-specific cross sections or dynamical diffraction. A sinusoidal 8 nm relief on a 160 nm period supplies local slopes; specimen relief alone is visually enlarged twofold. The two sector expectations are complementary in slope response; cancellation is exact only under this symmetric model after gain calibration. Right gain models independent count sensitivity, not multiplication of an already counted signal. Sum remains sensitive to grain orientation; normalized difference is a directional response, not height. No crystallographic indexing or quantitative elemental concentration.

Physics tutorial

BSE: Composition or Orientation?

BackgroundRecord both sides of a split detector. Calibrate their gains, switch between sum and difference, then rotate the specimen to separate material contrast, surface relief and prescribed channeling.

Why it mattersTarget: use the calibrated sum away from strong grain channeling. Material contrast error at most 0.03, asymmetry mean error at most 0.05, representative pixel CNR at least 8 and prescribed mean channeling suppression at most 3 percent.

Start with the essentials

Focus question: Can brighter grains prove a different composition?
One-sentence intuition: A brighter region can reflect material, orientation or collection geometry.

Core mathematical model

Count expectations

\begin{aligned}N_{inc}&=I\tau/e\\\mu_L&=N_{inc}\eta f(1-a)/2\\\mu_R&=g_RN_{inc}\eta f(1+a)/2\end{aligned}

The sector responses complement each other; gain is independent count sensitivity.

Process the same acquisition

\begin{aligned}\widehat Y&=\frac{N_L+N_R/g_R}{N_{inc}f}\\\widehat a&=\frac{N_R/g_R-N_L}{N_R/g_R+N_L}\end{aligned}

The sum retains material and orientation response; difference is a direction diagnostic.

Declared teaching response

\begin{aligned}\eta(Z)&=0.04+0.45(1-e^{-Z/30})\\c(\alpha,\alpha_g)&=1-0.22e^{-\frac{(\alpha-\alpha_g)^2}{18}}\end{aligned}

Prescribed yield and rocking dip, not a calculated material cross section.

Common difficulties

Separate appearance from information

Typical misconceptionA clearer-looking image guarantees the right interpretation.

Better mental modelDisplay gain does not change counts or undo physical mixing. The input reference is separate from measurement.

Run the experiment

01
Predict the ambiguity
Inspect the one-sided image and separate material and orientation inputs. Predict which stripes will change on rotation.
What to observe: Brightness contains several physical responses at once.
02
Calibrate before combining
Use the uncalibrated preset, then apply known gain calibration. Compare the asymmetry audit.
What to observe: Unequal sectors leak common response into their difference.
03
Rotate the specimen
Sweep rocking tilt through the two prescribed grain dips, then away from both.
What to observe: The sum cancels symmetric relief but still sees orientation.
04
Check the measurement
Choose the sum, calibrate, avoid grain dips and use enough dwell to meet the target.
What to observe: A composition claim needs controls and a noise budget.

Core mathematical model

Count expectations

Process the same acquisition

Declared teaching response

Common difficulties

Separate appearance from information

Run the experiment

Predict the ambiguity

Calibrate before combining

Rotate the specimen

Check the measurement