Chemistry Reference
In-Depth Information
X-ray
source
Detector
Divergence slit
Reflection angle 2θ
Layer
Incidence angle 2Ω
Substrate
FIGURE 7.18
Schematic diagram of x-ray reflectometry.
7.5.2 X-R
AY
R
EFLECTOMETRY
The measurement of x-ray reflectivity around the critical angle for total reflection
allows the accurate determination of film thickness, mass density, as well as surface
and interface roughness irrespective of the crystalline structure. X-ray reflectometry
is equally well applicable to crystalline, polycrystalline, and amorphous materials; it
only requires a sufficiently flat sample. The basic principle is shown in Figure 7.18.
It corresponds to the symmetrical Bragg-geometry. In the case of thin films on a
substrate constructive interference occurs between the beam reflected at the surface
and the beams reflected at the interfaces. Constructive interference results in intensity
maxima called
Kiessig fringes
, whose angular spacing is characteristic for the thick-
ness of the layers. The reflected intensity can be calculated by a recursive formula
taking the Fresnel coefficients for all corresponding interfaces into account. Using
Debye-Waller factor modified Fresnel coefficients to account the roughness in x-ray
reflectometry, the reflectivity of a layer can be calculated [68]. On the basis of such
an algorithm (Parrat recursive formula) the modeling of reflectometry measurements
yields thickness, surface and substrate roughness, and mass density.
A detailed description of x-ray methods for thin film analysis was recently pre-
sented by Wulff and Steffen [69]. Grazing incidence x-ray diffractometry (GIXD)
and x-ray reflectometry (XR) have been established as well-suiting tools for investi-
gations of chemical, physical, and crystallographic properties of thin films. They are
nondestructive techniques; therefore a sample can be reused and can be measured
with other techniques. A usable combination of GIXD and XR requires crystalline
films whose thickness does not exceed the upper physical absorption limit for the
reflectometry measurements.
Table 7.4 gives an overview of the possibilities of x-ray methods and alternative
techniques for thin film analysis.
7.6 RADICAL INVESTIGATION BY ELECTRON
SPIN RESONANCE
Radicals are atoms or molecules with one unpaired electron at least, and show
high chemical reactivity, for example, O
•
,NO
•
. Plasma-treated material surfaces or
