Scanning Electron Microscopy and X-Ray Microanalysis

382

23

There are two “zero-th level” assumptions that underpin the

basis for quantitative electron-excited X-ray microanalysis:

1. The only reason that the measured X-ray intensity differs
   between the unknown and the standard(s) is that the
   composition is different. No other factors such as the
   specimen shape, orientation, or size influence the
   measured X-ray spectrum.


2. The specimen is homogeneous in composition over the
   volume excited by the electron beam from which the
   characteristic and continuum X-rays are emitted,
   including the secondary radiation induced by absorption
   of the primary electron-excited radiation.

When either of these conditions is not met, a significant

increase in the overall uncertainty budget of the analysis can

occur beyond the ideal situation in which the uncertainties

arise from counting statistics and from uncertainties in the

calculated matrix correction factors.

Considering “zeroth-level” assumption 1, sample geom-

etry can significantly modify the measured X-ray intensity.

The ideal specimen is flat and placed at known angles to the

incident beam and the X-ray detector(s). Topographic fea-

tures on bulk specimens (defined as those for which the

thickness is much greater than the electron range) or

unusual geometric shapes, such as particles with dimensions

similar to the electron range, can strongly affect the mea-

sured X-rays by modifying X-ray generation and by affect-

ing the loss of X-rays due to absorption. In severe cases, the

impact of “geometric factors” on the final concentrations

becomes so large as to render the compositional results, as

calculated with the conventional standards-based/matrix

corrections protocol or the standardless protocol, nearly

worthless.

23.1 The Origins of “Geometric Effects”:

Bulk Specimens

The ideal sample is compositionally homogeneous on a

microscopic scale, has a flat surface, and is set at known

angles to the incident electron beam and the X-ray spectrom-

eter. Compared to the X-ray spectrum measured from this

ideal spectrum, geometric effects occur when the size and

shape of the specimen (1) modify the interaction of the elec-

trons with the specimen so as to affect the generated X-ray

intensity and (2) alter the length of the absorption path along

which the generated X-rays travel to escape the specimen and

reach the detector so as to affect the measured X-ray

intensity.

Because electron backscattering depends on the local sur-

face inclination to the incident beam, tilted samples generate

fewer X-rays compared to a sample at normal beam inci-

dence (0° tilt). An illustration of this effect for bulk copper, as

calculated with the Monte Carlo simulation embedded in

NIST DTSA-II, is shown in. Fig. 23.1. Even at normal beam

incidence where the backscattered electron (BSE) coefficient

is at a minimum, BSEs carry off energy which would have

gone to cause additional inner shell ionization events fol-

lowed by subsequent X-ray emission had those electrons

remained in the specimen. As the local surface inclination

(tilt) increases, backscattering increases and more X-ray gen-

eration is lost compared to normal beam incidence situation.

. Figure 23.2 shows Monte Carlo calculations of the Cu
K-L2,3 X-ray intensity emitted from a flat, bulk copper speci-
men, expressed as a “k-ratio,” where the denominator is the
intensity emitted from copper at zero tilt (normal beam inci-
dence). As the local surface inclination (tilt angle) increases
above zero degrees, the X-ray production decreases with

0

0.8

0.7

0.6

0.5

0.4

Backscatter coefficien

t

0.3

0.2

20 40

Tilt angle (degrees)

60 80

Cu E 0 = 20 keV

. Fig. 23.1 Backscatter coefficient η vs. surface tilt θ (inclination) for
Cu at E 0 = 20 keV as calculated with the Monte Carlo electron trajectory
simulation embedded in NIST DTSA-II

1.0

0.8

0.6

0.4

k-ratio

0.2

0.0

02040

Tilt angle (degrees)

60 80

Cu K-L2,3 emission vs. Tilt (E 0 = 20 keV)

. Fig. 23.2 Emitted Cu K-L2,3 X-ray intensity calculated as the k-ratio
relative to the intensity at a tilt of 0°, vs. surface tilt θ (inclination), for
Cu at E 0 = 20 keV as calculated with the Monte Carlo electron trajectory
simulation embedded in NIST DTSA-II

Chapter 23 · Analysis of Specimens with Special Geometry: Irregular Bulk Objects and Particles