Scanning Electron Microscopy and X-Ray Microanalysis

383 23

increasing tilt due to the increased backscattering seen in

. Fig. 23.1. There is a relatively small decrease in the k-ratio
at low tilt angles, but the k-ratio decreases rapidly for tilt
angles above approximately 40°. Because of the high photon
energy of Cu K-L2,3 (8.04 keV) and the relative transparency
of any material to its own X-rays, there is no significant
absorption so that the behavior shown in. Fig. 23.2 is almost
entirely due to the modification of the production of X-rays
due to backscatter loss.
Surface topography modifies the X-ray absorption path
length to the detector compared to a flat specimen at normal
beam incidence. As shown schematically in. Fig. 23.3, topo-
graphic features such as scratches and ridges can increase or
decrease the absorption path length in the direction of the
X-ray detector. X-ray absorption follows an exponential
dependence on this path length:

II/e 0 =−xp ()μ/ρρs

(23.1)

where I 0 is the initial intensity, I is the intensity that remains
after passing through a path length s (cm), (μ/ρ) is the mass
absorption coefficient (cm^2 /g) for the photon energy of interest
that depends on the absorption contributions of all elements
present, and ρ is the density (g/cm^3 ). Considering the entire
energy range of the generated X-ray spectrum, which extends
from a practical minimum threshold of 100 eV to the incident
beam energy, E 0 (the Duane–Hunt limit), as the X-ray photon
energy decreases, absorption generally increases. Absorption is
especially strong if the photon energy is less than 1 keV above
the critical ionization energy for any elemental constituent in
the specimen. An example of this effect is shown in. Fig. 23.4

for absorption as a function of path length for two contrasting

cases: Al K-L2,3 (1.487 keV) passing through Si (Kcrit = 1.838 keV),

and Si K-L2,3 (1.740 keV) passing through Al (Kcrit = 1.559 keV).

Because Si K-L2,3 is 0.181  keV above the critical ionization

energy for Al, Si is very strongly absorbed by Al (μ/ρ = 3282 cm^2 /g)

such that there is no penetration beyond approximately 6 μm.

By comparison, Al K-L2,3 is below the critical ionization energy

for Si, so it much less strongly absorbed (μ/ρ = 535 cm^2 /g), with

approximately 50% of  Al K-L2,3 intensity still remaining after

6-μm penetration through Si.

Geometric Effects: surface roughness affects local

absorption path to reach detector

Extended

absorption

path due to

ridge

Depth

of surface

scratch

Extended

absorption

path due to

scratch

Normal flat

bulk target

absorption

path

Reduced

absorption

path due to

scratch

Standard

I/I 0 = exp[-(μ/ρ)ρs]

ψ

. Fig. 23.3 Schematic illus-
tration of the effects of surface
topography on the X-ray absorp-
tion path length within the
specimen

X-ray absorption

0

0.0

0.2

0.4

I/I

0

0.6

0.8

1.0

24

Absorption path length (mm)

6810

Al K-L2,3 in Si

Si K-L2,3 in AI

. Fig. 23.4 Absorption as a function of path length for Al K-L2,3
(1.487 keV) passing through Si (Kcrit = 1.838 keV), and Si K-L2,3
(1.740 keV) passing through Al (Kcrit = 1.559 keV)

23.1 · The Origins of “Geometric Effects”: Bulk Specimens