E12 · Segmented SEM detection

BSE: Composition or Orientation?

Can brighter grains prove a different composition? Not on their own. A grain can look brighter in backscattered electrons because it contains heavier elements, because its crystal orientation changes how deep the beam channels in, or because its surface is tilted. Adding and subtracting the signals from two calibrated detector halves, and rotating the specimen, separate these causes.

Record counts on both halves of a split backscatter detector. Calibrate the two gains, switch between their sum and difference, then rock the specimen to tell material contrast apart from surface relief and the assumed channeling dips.

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

Contrast error against input $\text{—}$

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

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

More measurements and target

Stored left counts $\text{—}$

Stored right counts $\text{—}$

Separate unchanneled input contrast $\text{—}$

Prescribed mean channeling suppression $\text{—}$

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

Incident dose per pixel $\text{—}$

Experiment target $\text{—}$

Simulated examples; each plot identifies its data source.

Left-phase atomic number

Z_L

14

Right-phase atomic number

Z_R

29

Dwell per pixel

\tau

0.05\,\mathrm{ms}

Specimen rocking tilt about transverse axis

\alpha

8\,\mathrm{^\circ}

Advanced settings

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

Learning goal and model limits

Predict, then test it on the microscope

Can brighter grains prove a different composition?

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

Model assumptions

The counts are synthetic and drawn from a fixed random seed. The raster is 32 by 32 pixels with a 20 nm pitch and a 640 nm field, and the beam current is fixed at 20 pA. Dwell time is set per pixel, and collection efficiency is fixed at 15 percent. Counts with an expected value below 40 are Poisson samples; above 40 they use a normal approximation. The hardware and rays are schematic, but the rays do run from the source to the exposed specimen face and on to collectors above that same face. Display gain and the selected pixel reuse the stored counts. Monte Carlo electron transport, real detector calibration, contamination and damage kinetics are not modeled, and the Lab has no expert certification. The specimen has two assigned phases with independently selectable integer atomic numbers from 1 to 92 (initially 14 and 29), and each is made of grains that alternate between orientations of minus 8 and plus 8 degrees. The yield rises steadily with atomic number, and channeling shows up as Gaussian dips in the rocking curve; both are teaching assumptions, not material-specific cross sections or dynamical diffraction. A sinusoidal relief with an 8 nm amplitude and a 160 nm period sets the local slopes, and height and lateral distance share one scale. A slope adds to one sector's expected counts exactly what it takes from the other, so after gain calibration the sum cancels the relief exactly, but only in this symmetric model. The right-sector gain is that detector's own sensitivity; it does not multiply counts already recorded. The sum still depends on grain orientation, and the normalized difference measures which way the surface faces, not its height. The Lab does not index crystal orientations or measure element concentrations.

Physics tutorial

BSE: Composition or Orientation?

BackgroundA backscatter detector split into two halves records the specimen from two sides. You record counts on both halves, calibrate their gains, switch between sum and difference, then rock the specimen to tell material contrast apart from surface relief and the assumed channeling dips.

Why it mattersThe task is to use the calibrated sum and stay away from strong grain channeling. Reach a material contrast error of at most 0.03, a mean asymmetry error of at most 0.05, a contrast-to-noise ratio of at least 8 at a representative pixel, and an assumed mean channeling suppression of at most 3 percent.

Start with the essentials

Focus question: Can brighter grains prove a different composition?
One-sentence intuition: A region can look brighter because of its material, its crystal orientation or the way the detector collects electrons.

Core mathematical model

Expected counts in each sector

\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 local surface direction raises one sector's expected counts and lowers the other's by the same amount. The gain is the right detector's own sensitivity.

Sum and difference from the same counts

\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 keeps both the material signal and the orientation signal. The normalized difference shows which way the surface faces.

Assumed yield and channeling dip

\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}

The yield and the rocking dip are assumed teaching functions, not calculated material cross sections.

Common difficulties

A clearer image does not carry more information

Typical misconceptionIf the image looks clearer, my interpretation must be right.

Better mental modelDisplay gain does not change the counts, and it cannot unmix the physical effects. The input reference is shown separately and is not a measurement.

Run the experiment

01
Change composition while holding the geometry
Keep the calibrated sum at a rocking tilt of 30 degrees. Change Left-phase atomic number, then choose Brightness reversed. Predict the sign of the contrast before each change.
What to observe: The same detector geometry records a different material contrast. Swapping the two assigned phases reverses its sign; this comparison does not identify an unknown element.
02
Predict what will change
Look at the one-sided image next to the separate material and orientation inputs. Predict which stripes will change when you tilt the specimen.
What to observe: The brightness mixes several physical effects at once.
03
Calibrate before combining
Load the Uncalibrated sectors preset, then apply the known gain calibration. Compare the measured asymmetry with the known slope response.
What to observe: When the two sectors have unequal gains, signal common to both leaks into the difference.
04
Rotate the specimen
Set both atomic numbers to 29, then drag the specimen through the two assumed grain dips. Restore Separate the contrasts afterward.
What to observe: Grain stripes remain with equal composition. The sum cancels the symmetric relief, but it still responds to orientation.
05
Check the measurement
Choose the sum view, turn on calibration, stay away from the grain dips and raise the dwell until you meet the target.
What to observe: A claim about composition needs control comparisons and enough counts to rise above the noise.

Core mathematical model

Expected counts in each sector

Sum and difference from the same counts

Assumed yield and channeling dip

Common difficulties

A clearer image does not carry more information

Run the experiment

Change composition while holding the geometry

Predict what will change

Calibrate before combining

Rotate the specimen

Check the measurement