PRINCIPLES OF TOTAL REFLECTION XRF - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 94

Figure2.10. The normalized intensity I int / I 0 depending on glancing angle α and depth z. The
negative z values characterize the region below the surface inside the Si wafer. There is one single
antinode at z = 0 for α crit = 0.1 ° . For α > α crit , the intensity exponentially decreases with the
penetration depth z n , which is about 62 nm. For α < α crit , the intensity is evanescent within a
few nanometers. Figure from Ref. [10], reprinted with permission from the author.
This quantity may be of special interest. It is correlated to the minimum
penetration depth z 0 defined by Equation 1.79 for α << α crit . Both quantities
a crit and z 0 differ by the factor 2 π . Like the minimum depth z 0 , the period a crit is
also a material constant that is independent of the wavelength or photon energy
of the primary beam. Table 2.1 summarizes a crit and z 0 values calculated
according to Equations 2.18 and 1.80, respectively.
2.2.2StandingWaveFieldsWithinaThinLayer
Next to an infinitely thick substrate, a thin homogeneous layer on such a
substrate is of particular interest. The paths of X-rays for the two different
cases, A and B, have already been shown in Figure 2.1. Constructive or
destructive interference was demonstrated for the two reflected beams propa-
gating in the same direction. They result in Kiessig maxima and minima of the
reflectivity appearing for certain angles or directions , α k .
Both reflected beams not only interfere with each other, they also jointly
interfere with the incoming beam though propagating in a different direction.