Scanning Electron Microscopy and X-Ray Microanalysis

20

2

2.2.2 BSE Response to Specimen Inclination (η vs. Surface Tilt, θ)

Model the effect of the angle of inclination of the specimen sur-

face to the incident beam with the Monte Carlo simulation.

Select a particular element and incident beam energy, e.g., cop-

per and E 0 = 20 keV, and vary the angle of incidence. Calculate

at least 10,000 trajectories to obtain adequate simulation

precision.

. Figure 2.6 shows simulations for aluminum with an
incident beam energy of 15 keV at various inclinations calcu-
lated with 200 trajectories, which qualitatively reveals the
increase in backscattering in a forward direction (i.e., con-
tinuing in the general direction of the incident beam) with
increasing tilt angle. A more extensive series of simulations
for aluminum at E 0 = 15  keV with 25,000 trajectories cover-
ing a greater range of specimen tilts is presented in. Table 2.1,
where the backscatter coefficient shows a strong dependence
on the surface inclination.

Al

0 ∞ tilt

500 nm

E 0 = 15 keV

Al

500 nm

E 0 = 15 keV

45 ∞ tilt

AI

-1420.2 nm

AI

-710.0 nm -0.0 nm 710.0 nm 1420.0 nm

1950.1 nm

1462.6 nm

975.0 nm

487.5 nm

0.0 nm

-961.2 nm -480.6 nm -0.0 nm 480.6 nm 961.2 nm

1320.0 nm

990.0 nm

660.0 nm

330.0 nm

0.0 nm

a b

Al

500 nm

E 0 = 15 keV

60 ∞ tilt

Al

500 nm

E 0 = 15 keV

75 ∞ tilt

AI

-1223.3 nm -611.7 nm -0.0 nm 611.7 nm 1223.3 nm

1680.0 nm

1260.0 nm

840.0 nm

420.0 nm

0.0 nm AI

-699.0 nm -349.5 nm -0.0 nm 349.5 nm 699.0 nm

960.0 nm

720.0 nm

480.0 nm

240.0 nm

0.0 nm

c d

. Fig. 2.6 a Monte Carlo simulation for aluminum at E 0 = 15 keV for
a tilt angle of 0°. b Monte Carlo simulation for aluminum at E 0 = 15 keV
for a tilt angle of 45°. c Monte Carlo simulation for aluminum at

E 0 = 15 keV for a tilt angle of 60°. d Monte Carlo simulation for alumi-

num at E 0 = 15 keV for a tilt angle of 75°

. Table 2.1 Backscatter vs. tilt angle for aluminum at
E 0 = 15 keV (25,000 trajectories calculated with the CASINO
Monte Carlo simulation)

Tilt (degrees) η

0 0.129

15 0.138

30 0.169

45 0.242

60 0.367

75 0.531

80 0.612

85 0.706

88 0.796

89 0.826

Chapter 2 · Backscattered Electrons