Use of X-ray Reflectivity to Measure Thickness, Roughness and Density
Introduction
X-rays exhibit total external reflection when impinged on a sample below a critical incidence angle. The critical angle is related to film density. As the angle of reflection is increased above the critical angle, X-ray penetration occurs and reflections from sub-surface layers interfere with surface reflected radiation causing interference fringes indicating thickness and interfacial roughness. Because this technique does not rely upon material crystallinity, it can be used to characterize amorphous as well as crystalline layers.
Density
The density of the material being measured determines the critical angle, below which there is total external reflection, and above which internal reflection occurs due to X-ray penetration. In addition to material density, the wavelength of the X-ray radiation also determines the critical angle. If either the density or the wavelength increases, there is a corresponding increase in the critical angle that is measured.
Ru on Si – Ru density: 12.4 g/cm3
SiO2 on Si – SiO2 density 2.6 g/cm3
Thickness and Roughness
500A W on 1000A SiO2
The appearance of the finely spaced interference fringes is determined by both the thickness (oscillation frequency) and the interfacial roughness (decreasing amplitude at high angle) of each layer. The amplitude of oscillation is also indicative of the density contrast between layers. The decreasing intensity at high angle is due predominantly to the surface roughness.
Modelling
400A Ta on Si
The key to analysis of XRR data is the modelling software used to fit the data. At Cerium Labs we use REFS Mercury written by Bede, the manufacturer of our XRR instrument and an industry leader in x-ray metrology. This software applies a generic algorithm to fit the data while allowing the Roughness, Thickness and Density numbers to vary independently until a best fit is obtained. TEM measurements have verified the accuracy of the fitting algorithms. The example above is a nominal 400A Ta film on Si. The fit shows excellent agreement between the experimental data and the fitted (modelled) data. The model shows the Ta film being 383A thick with a 25A Ta2O5 oxide layer on top. The roughness of the Ta layer is 3.5A (RMS type measurement) and a density of 16.6 g/cm3.
X-ray Conditions
Bede D-3 Diffractometer
Omega-2Theta scans: 0-7200 Arcseconds, 10 arcsecond steps
Power: 40 kV, 200 mA Rotating Cu Anode
Detector Slits: Front 0.5 mm; Rear 1.0 mm;
Double Crystal - High Resolution Mode
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