50 Experimental Methods
Figure 3.4: Illustration of the interaction between X-ray radiation and a crystal
lattice that can lead to constructive interference. For specic angles and interplanar
distances the Bragg conditions are fullled and this can be detected in an XRD
measurement.
where K is a shape factor, with a typical value of 0.9, is the wavelength of
the X-rays, is the line broadening at full width half maximum (FWHM) and
the Bragg angle as mentioned above. Another important parameter is the
instrumental line broadening which should be subtracted from the measured
line broadening to get . It should also be noted that a domain size found from
the Scherrer equation gives a lower bound and works best when the domains
are all the same size. This is due to other factors which could contribute to
the broadening. If there are a spread in the size the smaller domains could
give rise to a broadening, but the larger will dominate the signal. To estimate
the instrumental line broadening as function of a silicon reference sample was
measured.
All measurements presented here were acquired with a PANalytical X'Pert Pro
equipment with an X-ray wavelength of 1.54 Å for the CuK line.
3.2.2.1 Glancing Angle X-Ray Diraction
As XRD is a bulk sensitive technique it can be challenging to obtain information
about thin lm samples with acceptable signal to noise. Naturally, this depends
on the thickness of the lm, typically 10-100 nm in this project, but often
the substrate will contribute with a large signal. This issue can be somewhat
mitigated by using the Glancing Angle technique, GA-XRD, where the incoming
X-rays are always kept at a low angle, 195. A schematic of this technique
can be seen in gure 3.5.
By choosing a suciently low incoming angle the signal contribution from
the substrate can be minimized due the penetration depth of the X-rays. Although
useful, the higher surface selectivity comes at a cost since it puts some