X-ray reflectivity
Encyclopedia
X-ray reflectivity sometimes known as X-ray specular reflectivity, X-ray reflectometry, or XRR, is a surface-sensitive analytical technique used in chemistry
, physics
, and materials science
to characterize surfaces, thin films and multilayers. It is related to the complementary techniques of neutron reflectometry
and ellipsometry
.
The basic idea behind the technique is to reflect a beam of x-ray
s from a flat surface and to then measure the intensity of x-rays reflected in the specular direction (reflected angle equal to incident angle). If the interface is not perfectly sharp and smooth then the reflected intensity will deviate from that predicted by the law of Fresnel reflectivity. The deviations can then be analyzed to obtain the density profile of the interface normal to the surface.
The technique appears to have first been applied to x-rays by Professor Lyman G. Parratt of Cornell University in an article published in Physical Review
in 1954. Parratt's initial work explored the surface of copper-coated glass, but since that time the technique has been extended to a wide range of both solid and liquid interfaces.
The basic mathematical relationship which describes specular reflectivity is fairly straightforward. When an interface is not perfectly sharp, but has an average electron density profile given by
, then the x-ray reflectivity can be approximated by :
Here
is the reflectivity, 
, 
is the x-ray wavelength, 
is the density deep within the material and 
is the angle of incidence. Typically one can then use this formula to compare parameterized models of the average density profile in the z-direction with the measured x-ray reflectivity and then vary the parameters until the theoretical profile matches the measurement.
For films with multiple layers, X-ray reflectivity may show oscillations with wavelength, analogous to the Fabry-Pérot effect. These oscillations can be used to infer layer thicknesses and other properties, for example using the Abeles matrix formalism.
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, and materials science
Materials science
Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. This scientific field investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It incorporates...
to characterize surfaces, thin films and multilayers. It is related to the complementary techniques of neutron reflectometry
Neutron Reflectometry
Neutron reflectometry is a neutron diffraction technique for measuring the structure of thin films, similar to the often complementary techniques of X-ray reflectivity and ellipsometry...
and ellipsometry
Ellipsometry
Ellipsometry is an optical technique for the investigation of the dielectric properties of thin films....
.
The basic idea behind the technique is to reflect a beam of x-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s from a flat surface and to then measure the intensity of x-rays reflected in the specular direction (reflected angle equal to incident angle). If the interface is not perfectly sharp and smooth then the reflected intensity will deviate from that predicted by the law of Fresnel reflectivity. The deviations can then be analyzed to obtain the density profile of the interface normal to the surface.
The technique appears to have first been applied to x-rays by Professor Lyman G. Parratt of Cornell University in an article published in Physical Review
Physical Review
Physical Review is an American scientific journal founded in 1893 by Edward Nichols. It publishes original research and scientific and literature reviews on all aspects of physics. It is published by the American Physical Society. The journal is in its third series, and is split in several...
in 1954. Parratt's initial work explored the surface of copper-coated glass, but since that time the technique has been extended to a wide range of both solid and liquid interfaces.
The basic mathematical relationship which describes specular reflectivity is fairly straightforward. When an interface is not perfectly sharp, but has an average electron density profile given by
, then the x-ray reflectivity can be approximated by :Here
is the reflectivity, , is the x-ray wavelength, is the density deep within the material and is the angle of incidence. Typically one can then use this formula to compare parameterized models of the average density profile in the z-direction with the measured x-ray reflectivity and then vary the parameters until the theoretical profile matches the measurement.For films with multiple layers, X-ray reflectivity may show oscillations with wavelength, analogous to the Fabry-Pérot effect. These oscillations can be used to infer layer thicknesses and other properties, for example using the Abeles matrix formalism.