PRINCIPLES OF TOTAL REFLECTION XRF - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 107

Figure2.19. Fluorescence intensity from layers buried in a thick substrate. The intensity dependent
on the glancing angle was calculated for layers of different thickness but with a constant area density
of the analyte. Silicon was assumed as the substrate, Mo-K α X-rays, as the primary beam. Total
reflection occurs in the region below 0.1 ° . Without total reflection, the dashed horizontal line would be
valid in all. Figure from Ref. [1], reproduced with permission. Copyright1996, John Wiley and Sons.

Equations 2.15, 2.19, and 2.20, and can be approximated by

2

p

R α

α
α crit

I BL α

≅ I n c A 4

(2.24)

in the region of total reflection α α crit , and by

p

R α

2

I BL α ≅ I n c A 1 (2.25)

in the region beyond total reflection. The first approximation represents a
parabola with a maximum intensity of nearly 4 I n c A at the critical angle. The
second equation describes an asymptotic decrease of the curve to a constant
value I n c A at larger angles as illustrated by Figure 2.19.
For layers of several 100 nm, the thickness d far exceeds the penetration
depth z n . In this case the peaks at the critical angle are reduced and the curves
of Figure 2.19 get an S-like shape. Equation 2.22 can be approximated by

α
d

I BL α

≅ I n c A C 1

R α (2.26)

with symbols as defined earlier.