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