X-ray reflectivity

What is XRR analysis used for?

X-ray reflectivity (XRR), also known as X-ray specular reflectivity or X-ray reflectometry, is a common thin film characterization technique. With XRR, it is possible to determine the thickness, density, and roughness of films composed of different materials, such as semiconductive, magnetic, and optical materials.

Both crystalline (single crystal or polycrystalline) and amorphous matter in very thin layers can be analyzed, and materials can have single or multiple layers or coatings. The properties of both the surface of the material and the interfaces of the layers can be determined using X-ray reflectivity.

What is the working principle of XRR?

In XRR analysis, the flat surface of the sample is irradiated with a beam of X-rays at such angles of incidence that they only graze the surface. When the X-rays hit the surface of the sample, they are reflected by the electrons of the atoms in the sample. The total reflection angle of the X-ray beam occurs at or below a critical angle, θ. This critical angle is very small and that is why also the angles of the reflected X-rays are extremely low. The critical angle varies depending on the electron density of the material used. 

The higher the incident angle of the X-ray beam hitting the sample relative to the critical angle of the reflected X-rays, the deeper the X-rays go down into the material. The incident and reflection angles of the X-rays are always equal. Therefore, if the angle of total reflection of X-rays is smaller than the critical angle, X-rays go through the sample only a few nanometers, but when the reflection angle rises above the critical angle the depth of the penetrating X-rays increases rapidly. 

The XRR analyzer measures the intensity of the reflected X-rays (reflectivity of the material) in such a direction, where the reflection angle of the X-rays is equal to the grazing incident angle of the original X-rays. When analyzing a material whose surface is ideally flat, the reflectivity of the material suddenly decreases when the angle of the reflected X-ray beam rises above the critical angle of the material and the depth of the penetrating X-rays increases. If the surface of the material is rough, the reflectivity decreases more drastically when the reflection angle of the X-rays rises. 

Information deduced from the intensity of the reflected X-rays

In case the interface between two layers in the material (a coating layer and the substrate) is not perfectly sharp and smooth, the intensity of the reflected X-rays will deviate from the predicted value according to the law of Fresnel reflectivity. The intensity of the reflected X-rays is approximately proportional to the square of the modulus of the Fourier transform of the electron density. Therefore the electron density profile of the material can be deduced from the measured intensity pattern of the reflected X-rays with the help of the Fourier transform.

By analyzing the deviations of the reflected X-rays' intensity, the density profile of the interface normal to the surface of the sample can be produced. The individual layer parameters such as thickness and density as well as interface and surface roughness can be determined from the reflectivity curves of the material. Thus the lateral properties, such as roughness and correlation properties of interfaces or lateral layer structure, can be deduced from the measured intensity pattern.

Information deduced from the interference of the reflected X-rays

At every interface of individual films of the material where the electron density changes even a little, only a part of the X-ray beam is reflected. If a rough material is used as a substrate and evenly coated with another material, the reflected X-rays of the different materials will interfere with each other. This happens because the X-rays reflected from different surfaces (the interface of the substrate and the coating, and the free surface of the top layer) have traveled different distances and thus they are in different phases.

The interference happens either constructively (the rays amplify each other) or destructively (the rays deaden each other). This phenomenon creates an interference-induced oscillation pattern which is observed during the analysis. The vertical properties, that is the thicknesses of the layers, can be determined from the periodicity of the oscillation pattern. Information about the surface of the material and the possible interface of two materials (e.g. roughness) can be deduced from the angular dependency of the amplitude of the oscillation pattern. 

Need an XRR analysis?

Measurlabs offers high-quality XRR analyses at an affordable price. You always get help from our team of experts if you have any questions related to your samples or the suitability of the method for your needs. Contact us through the form below or by email to info@measurlabs.com to get started!