International Tables for Crystallography

Thin films and multilayers
M. Birkholz. International Tables for Crystallography (2019). Vol. H, ch. 5.4, pp. 581-600  [ doi:10.1107/97809553602060000969 ]


In thin-film work, the weak interaction of X-rays with matter because of their high energies has important consequences. Since the film's thickness t is generally much smaller than its inverse attenuation coefficient 1/μ, the diffraction pattern is strongly affected by absorption effects, and the product μt turns out to be the central physical parameter in thin-film diffraction. The variation of absorption with scattering angle 2θ allows one to elucidate interesting properties of the sample, such as microstructure, voids, contaminants and possible amorphous fractions. Grazing-incidence techniques have been developed in order to extend the interaction path of the X-ray beam within the sample. By varying the information depth of the beam through variation of the incidence angle αi, such techniques reveal that the structure of thin films, their crystallographic texture, and their stress and strain state depend strongly on layer depth and evolve with increasing thickness. Important complementary information on the layer's depth-dependent electron density can be obtained using the non-diffraction technique of X-ray reflectivity. The methods are outlined in this chapter and illustrated by examples from relevant branches of technology, such as optics, microelectronics, superconductivity, photovoltaics and hard coatings etc., to which results from X-ray scattering from thin films and multilayers have made important contributions.

Access, prices and ordering

International Tables for Crystallography is available online as a full set of volumes through Wiley.


If you have already registered and are using a computer listed in your registration details, please email for assistance.

About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.