1. Reflectivity Measurements on Non-ideal Surfaces
In this presentation reflectivity measurements on curved or undulated surfaces are described.
Note to the presenter: The complete story of this presentation is described in the Philips Analytical Application Note “Application of a Beam-Knife in Reflectivity Measurements on non-ideal Surfaces” ( ).

2. Reflectivity Measurements on Non-ideal Surfaces
Contents:
Application
Method
Alignment
GIXR on Undulated Samples
Example
Conclusions
After a short introduction into possible application areas for reflectivity measurements the method is described.
Afterwards the alignment procedure and the possible problems arising with not perfectly flat samples during the alignment and in reflectivity measurements are discussed.
The instrumentation for the measurement of such samples is shown and an example will show the advantage of the described reflectivity set-up.
The presentation will end with a summary.

3. X-ray reflectivity Measurement on thin layers to determine:
GIXR on non-ideal surfaces
Measurement on thin layers to determine:
Layer thickness
Density
Interface roughness
Inter-diffusion effects
Grazing incidence X-ray reflectivity (GIXR) extends the area of analysing methods for thin layers. It allows the determination of many important characteristic parameters as layer thickness, interface roughness, layer density and inter-diffusion effects between layers.

4. Method (1)
Sample reflectivity measured around critical angle of total reflection c
n1= 1  n2 d
 2 n3
This figure shall illustrate the principle of the measurement.
In Grazing incidence X-ray reflectivity (GIXR) measurements the reflectivity of sample surfaces is measured around the critical angle of total reflection c.
The critical angle is related to the electron density of the reflecting medium.
Below the critical angle X-rays penetrate only a few nanometers into the sample (typically nm) whereas above this angle the penetration depth increases rapidly.
Below c beam penetrates only few nm
Above c penetration increases sharply

5. Method (2) Permits surface/layer analysis
Partial reflection at each layer interface
Interference of reflected beams creates oscillations in reflectivity curves
n1= 1  n2 d n3
 2
At every interface where the electron density changes, a part of the X-ray beam is reflected. The interference of this partially reflected X-ray beams create the oscillations shown in reflectivity measurements.
Thus the spacing of the oscillations gives information about the layer thickness.
Grazing incidence X-ray reflectivity (GIXR) therefore can be used to analyse sample surfaces and thin layers.
Permits surface/layer analysis

6. Alignment (1) Accurate alignment to incident beam essential
For high-accuracy measurements of well-defined sample area necessary
For reflectivity measurements an accurate adjustment of the sample according to the incident beam is very important. As a start, the alignment is done with respect to the incident beam by performing a rocking curve measurement.
For higher accuracy an additional alignment at one (or even) several different other -angles of the sample (e.g. just below the critical angle or at a fringe position of the reflectivity curve) are necessary. The alignment should be done with an accuracy of approximately 0.001o in .
As already pointed out the determination of the critical angle c gives the electron density and, with known stochiometric composition, the mass density of the reflecting medium. To determine this angle with high accuracy, experimental data of a well defined sample area are required to be fitted with a simulation program.

7. Alignment (2)
Problem:
Curved/undulating/irregular surfaces cause rocking curve broadening, deformation - preventing accurate adjustment
The described alignment procedure works very well for flat samples. But irregularly shaped samples cause problems during the alignment procedure or prevent the measurement of a well-defined sample area.
Un-ideal and wavy sample surfaces cause changes in the rocking curve shape compared to flat surfaces. This prevents an accurate adjustment.
Such undulant samples occur in a wide range of application areas.
In this presentation reflectivity measurements of curved glass surfaces and of oxide layers on these samples are described. Due to some production processes the shape of glass surfaces is generally not perfectly flat but bent or waved. These surface shapes sometimes cause problems with the alignment of the sample and cause changes in the intensity near the critical angle in a reflectivity measurement.

8. Alignment (3)
Solution:
Add a beam knife

9. GIXR on Undulated Samples (1)
A beam-knife may solve these problems as will be shown in the following part of the demonstration.

10. GIXR on Undulated Samples (2)
This picture shows the beam knife used in a Philips X’Pert PRO MRD.
It is mounted on the cradle perpendicularly to the sample surface. It allows the adjustment of the tilt parallel to the sample surface and an accurate adjustment of the distance between knife and sample surface.

11. GIXR on Undulated Samples (3)
GIXR on non-ideal surfaces
Philips
X’Pert PRO
Materials
Research
Diffractometer
This figure shows a typical experimental set-up used for reflectivity measurements with beam knife in an Philips X’Pert PRO Materials Research Diffractometer (MRD) system. This set-up was used for the measurements shown in this presentation.
The X’Pert PRO Diffractometer allows a highly accurate adjustment of the sample with respect to the incident beam and - using an automatic beam attenuator - the measurement of a large dynamic intensity range.
Both instrumental aspects are most important for reflectivity measurements.
The beam knife above the sample limits the effective reflecting sample area. The distance to the sample is adjusted in a way that the beam knife cuts approximately 30% of the intensity (it might be more, depending on the sample curvature).

12. GIXR on Undulated Samples (4)
Rocking curves used for alignment
These figures show rocking curves of a curved sample in the incident beam (the picture is similar for concave and convex samples) and of an irregularly shaped sample at an angle just below the critical angle, with and without a beam knife.
This demonstrates that for an accurate alignment of a curved sample the beam knife is strongly desirable or even necessary. The rocking curves of bent samples (without usage of a beam knife) are often strongly broadened, deformed or sometimes there is even no reasonable signal. In contrast the measurements with beam knife show small single peaks in the rocking curves enabling a good alignment.
Whereas flat samples can be measured without a beam knife, measurements on curved samples might be only possible with it.
Curved sample
Irregular sample

13. Example Ta2O5 on SiO2 GIXR on non-ideal surfaces
The purpose of this example is to show that the beam knife does not interfere with the quality of the data. Therefore a sample has been chosen which still could be measured without a beam knife as well.
The graphs show the comparison of reflectivity measurements of a Ta2O5 layer deposited on a slightly bent SiO2-substrate with and without a beam knife. Both the area around the critical angle and a larger angular range exhibiting fringes are displayed. The measurement time of both measurements has been the same. Therefore the statistic is slightly different (lower intensity with beam knife).
The measurement shows that the beam knife improves the shape of the graph near the critical angle, whereas the shape of the curve above the critical angle is not noticeably changed. The improved shape (flat plateau) can be used for accurate normalisation of the graph which is necessary for a good fit. Therefore the use of the beam knife allows the determination of the critical angle - and therewith the density of the reflecting material - with better accuracy. Small differences in the shape of the curve at higher -angles are due to the reduction of the diffuse scattering by use of the beam knife.

14. Conclusions
Beam knife allows accurate alignment of irregularly shaped samples
Improves graph shape near critical angle (necessary for accurate normalization and good fit of graph)
Beam knife sometimes essential to allow measurements on curved samples
X-ray reflectivity (GIXR) offers a powerful non-destructive tool to characterise thin layers. The profit and/or necessity to use a beam knife for these measurements depends strongly on the flatness and surface quality of the sample.
The beam knife allows the accurate alignment of undulant or curved samples and can improve the shape of the “plateau” in reflectivity curves below the critical angle. This allows the determination of the critical angle and therefore the calculation of the material’s density with higher accuracy.
Therefore the beam knife is sometimes essential for measurements of curved samples.